���A���>�3�7���Dx����M�>�F��h�7Ut�y�~!G"�*)�J����l=4�#:>09:I�]�A$9���e��v � ���y���;8���z�P�@0�].o��K�y]�V}��ݿ+�1Y�d�$���yQ���� }>����ڏ[�x��}8��֛=1���8��O{t�kV�z=���� for being eligible to sit for this exam include being between the ages of 19 Play as . However, in the MFAT market, the Military Flight Aptitude Test is the best. the Americans with Disabilities Act, be sure to talk to your recruiter about 5- If \(\theta\) is an acute angle and sin \(\theta = \frac{3}{5}\), then cos \(\theta\) =? 5. Which of these is not a criterion for classifying an aircraft? Effortless Math services are waiting for you. Each piece of DNA is described using either A, C, G, or T. Each component is organized in a unique and particular order. The sample math questions you’ll find here are brief samples designed to give you the insights you need to be as prepared as possible for your ASTB Math test. Topics include: Reading Comprehension, Math, Mechanical Comprehension, Nautical Information and Aviation, and much more. Directions: Below are 5 passages each with four possible answer choices. A) C D) Reduce landing weight, A) North Pole Then, you’ll not only find the correct answers, but do it quickly as well. Its been made by Barron’s, one of the tops in the industry and is well organized. Instead, these questions are meant to familiarize examinees with the format and content of questions found within each section. Test takers are assessed on their knowledge of principles related to liquids and gases, as well as their understanding of how liquids and gases affect volume, pressure, and velocity in the Mechanical Comprehension Test of the ASTB. Immediately after completing all seven subtests, you will receive your score report. B) Video conferencing is more economically feasible than traditional face-to-face meetings endobj During the Quiz End of Quiz. The Performance Based Measures Battery will assess your ability to complete listening tasks, answer directional items, and accomplish tracking tasks. A) Documents can be damaged by rust A) 4A + B = 10 The performance of an individual in this examination determines if he/she meets the standards for training. endobj Feedback. Time to Complete: 10 min. Save my name, email, and website in this browser for the next time I comment. © 2020 Study Guide Zone. 1- CMETHOD ONE\(log_4⁡(x+2) – log_4⁡(x-2) = 1\)Add \(log_4⁡(x-2)\) to both sides\(log_4⁡(x+2) – log_4⁡(x-2)+ log_4⁡(x-2)= 1 + log_4⁡(x-2)\)\(log_4⁡(x+2) = 1 + log_4⁡(x-2)\)Apply logarithm rule:\(a = log_b⁡(b^a) ⇒ 1 = log_4⁡(4^1) = log_4⁡(4)\)then: \(log_4⁡(x+2) = log_4⁡(4) + log_4⁡(x-2)\)Logarithm rule: \(log_c⁡(a) + log_c⁡(b) = log_c⁡(ab)\)then: \(log_4⁡(4) + log_4⁡(x-2) = log_4⁡(4(x-2))\)\(log_4⁡(x+2) = log_4⁡(4(x-2))\)When the logs have the same base:\(log_b⁡(f(x)) = log_b⁡(g(x)) ⇒ f(x) = g(x)(x+2) = 4(x-2)\)\(x = \frac{10}{3}\)METHOD TWOWe know that:\(log_a⁡b-log_a⁡c=log_a\frac{b}{c}⁡\space and \space log_a⁡b=c⇒b=a^c\)Then: \(log_4⁡(x+2)- log_4⁡(x-2)=log_4\frac{(x + 2)}{(x – 2)}⁡=1⇒\frac{(x + 2)}{(x – 2)}=4^1=4⇒x+2=4(x-2)⇒x+2=4x-8⇒4x-x=8+2→3x=10⇒x=\frac{10}{3}\), 2- B\(e^{(5x + 1 )}= 10\)If \( f(x) = g(x)\), then \(ln(f(x)) = ln(g(x))\)\(ln⁡(e^{(5x + 1 )})= ln(10)\)Apply logarithm rule:\(log_a⁡(x^b) = b log_a⁡(x)\)\(ln⁡(e^{(5x + 1 )})= (5x + 1)ln(e)\)\((5x + 1)ln(e) = ln(10)\)\((5x + 1)ln(e) = (5x + 1)\)\((5x + 1) = ln(10) \)\( ⇒x = \frac{ln⁡(10) – 1}{5}\), 3- C\(f(x) = x –\frac{5}{3}⇒ y = x – \frac{5}{3}⇒ y+ \frac{5}{3}=x\)\(f^{-1 }= x+ \frac{5}{3}\)\(f ^{–1}(5) = 5 +\frac{5}{3}=\frac{20}{3}\), 4- Ccos \(30^{\circ} = \frac{\sqrt 3}{2}\), 5- Csin\(θ=\frac{3}{5}⇒\) we have following triangle, then:\(c=\sqrt {(5^2-3^2 )}=\sqrt{(25-9)}=\sqrt 16=4\)cos\(θ=\frac{4}{5}\), 6- B\(-2x- y = -9\)\(5x-2y= 18\)\(⇒\) Multiplication \((–2)\) in first equation\(4x +2y =18\)\(5x-2y= 18\)Add two equations together \(⇒ 9x =36 ⇒ x= 4\) then: \(y = 1\), 7- C\(|9 – (12 ÷ | 2 – 5 |)| = |(9-(12÷|-3|))|=|9-(12÷3)|=|9-4|=|5|=5\), 8- DMETHOD ONE\(log_{2}⁡x = 5\)Apply logarithm rule: \(a = log_b⁡(b^a)\)\(5 = log_2⁡(2^5) = log_2⁡(32)\)\(log_2⁡x = log_2⁡(32)\)When the logs have the same base: \(log_b⁡(f(x)) = log_b⁡(g(x))⇒ f(x) = g(x)\)then: \(x = 32\)METHOD TWOWe know that:\(log_a⁡b=c⇒b=a^c \)\(log_2⁡x=5⇒x=2^5=32\), 9- D\(\frac{x^3}{16}\)\(⇒\) reciprocal is : \(\frac{16}{x^3}\), 10- A\(f(x) = ln (2x + 1)\)\(y = ln (2x + 1)\)Change variables \(x\) and \(y: x = ln (2y + 1)\)solve: \(x = ln (2y + 1)\)\(y = \frac{e^{x}-1}{2}=\frac{1}{2}(e^{x} – 1)\), Your email address will not be published. "/> ���A���>�3�7���Dx����M�>�F��h�7Ut�y�~!G"�*)�J����l=4�#:>09:I�]�A$9���e��v � ���y���;8���z�P�@0�].o��K�y]�V}��ݿ+�1Y�d�$���yQ���� }>����ڏ[�x��}8��֛=1���8��O{t�kV�z=���� for being eligible to sit for this exam include being between the ages of 19 Play as . However, in the MFAT market, the Military Flight Aptitude Test is the best. the Americans with Disabilities Act, be sure to talk to your recruiter about 5- If \(\theta\) is an acute angle and sin \(\theta = \frac{3}{5}\), then cos \(\theta\) =? 5. Which of these is not a criterion for classifying an aircraft? Effortless Math services are waiting for you. Each piece of DNA is described using either A, C, G, or T. Each component is organized in a unique and particular order. The sample math questions you’ll find here are brief samples designed to give you the insights you need to be as prepared as possible for your ASTB Math test. Topics include: Reading Comprehension, Math, Mechanical Comprehension, Nautical Information and Aviation, and much more. Directions: Below are 5 passages each with four possible answer choices. A) C D) Reduce landing weight, A) North Pole Then, you’ll not only find the correct answers, but do it quickly as well. Its been made by Barron’s, one of the tops in the industry and is well organized. Instead, these questions are meant to familiarize examinees with the format and content of questions found within each section. Test takers are assessed on their knowledge of principles related to liquids and gases, as well as their understanding of how liquids and gases affect volume, pressure, and velocity in the Mechanical Comprehension Test of the ASTB. Immediately after completing all seven subtests, you will receive your score report. B) Video conferencing is more economically feasible than traditional face-to-face meetings endobj During the Quiz End of Quiz. The Performance Based Measures Battery will assess your ability to complete listening tasks, answer directional items, and accomplish tracking tasks. A) Documents can be damaged by rust A) 4A + B = 10 The performance of an individual in this examination determines if he/she meets the standards for training. endobj Feedback. Time to Complete: 10 min. Save my name, email, and website in this browser for the next time I comment. © 2020 Study Guide Zone. 1- CMETHOD ONE\(log_4⁡(x+2) – log_4⁡(x-2) = 1\)Add \(log_4⁡(x-2)\) to both sides\(log_4⁡(x+2) – log_4⁡(x-2)+ log_4⁡(x-2)= 1 + log_4⁡(x-2)\)\(log_4⁡(x+2) = 1 + log_4⁡(x-2)\)Apply logarithm rule:\(a = log_b⁡(b^a) ⇒ 1 = log_4⁡(4^1) = log_4⁡(4)\)then: \(log_4⁡(x+2) = log_4⁡(4) + log_4⁡(x-2)\)Logarithm rule: \(log_c⁡(a) + log_c⁡(b) = log_c⁡(ab)\)then: \(log_4⁡(4) + log_4⁡(x-2) = log_4⁡(4(x-2))\)\(log_4⁡(x+2) = log_4⁡(4(x-2))\)When the logs have the same base:\(log_b⁡(f(x)) = log_b⁡(g(x)) ⇒ f(x) = g(x)(x+2) = 4(x-2)\)\(x = \frac{10}{3}\)METHOD TWOWe know that:\(log_a⁡b-log_a⁡c=log_a\frac{b}{c}⁡\space and \space log_a⁡b=c⇒b=a^c\)Then: \(log_4⁡(x+2)- log_4⁡(x-2)=log_4\frac{(x + 2)}{(x – 2)}⁡=1⇒\frac{(x + 2)}{(x – 2)}=4^1=4⇒x+2=4(x-2)⇒x+2=4x-8⇒4x-x=8+2→3x=10⇒x=\frac{10}{3}\), 2- B\(e^{(5x + 1 )}= 10\)If \( f(x) = g(x)\), then \(ln(f(x)) = ln(g(x))\)\(ln⁡(e^{(5x + 1 )})= ln(10)\)Apply logarithm rule:\(log_a⁡(x^b) = b log_a⁡(x)\)\(ln⁡(e^{(5x + 1 )})= (5x + 1)ln(e)\)\((5x + 1)ln(e) = ln(10)\)\((5x + 1)ln(e) = (5x + 1)\)\((5x + 1) = ln(10) \)\( ⇒x = \frac{ln⁡(10) – 1}{5}\), 3- C\(f(x) = x –\frac{5}{3}⇒ y = x – \frac{5}{3}⇒ y+ \frac{5}{3}=x\)\(f^{-1 }= x+ \frac{5}{3}\)\(f ^{–1}(5) = 5 +\frac{5}{3}=\frac{20}{3}\), 4- Ccos \(30^{\circ} = \frac{\sqrt 3}{2}\), 5- Csin\(θ=\frac{3}{5}⇒\) we have following triangle, then:\(c=\sqrt {(5^2-3^2 )}=\sqrt{(25-9)}=\sqrt 16=4\)cos\(θ=\frac{4}{5}\), 6- B\(-2x- y = -9\)\(5x-2y= 18\)\(⇒\) Multiplication \((–2)\) in first equation\(4x +2y =18\)\(5x-2y= 18\)Add two equations together \(⇒ 9x =36 ⇒ x= 4\) then: \(y = 1\), 7- C\(|9 – (12 ÷ | 2 – 5 |)| = |(9-(12÷|-3|))|=|9-(12÷3)|=|9-4|=|5|=5\), 8- DMETHOD ONE\(log_{2}⁡x = 5\)Apply logarithm rule: \(a = log_b⁡(b^a)\)\(5 = log_2⁡(2^5) = log_2⁡(32)\)\(log_2⁡x = log_2⁡(32)\)When the logs have the same base: \(log_b⁡(f(x)) = log_b⁡(g(x))⇒ f(x) = g(x)\)then: \(x = 32\)METHOD TWOWe know that:\(log_a⁡b=c⇒b=a^c \)\(log_2⁡x=5⇒x=2^5=32\), 9- D\(\frac{x^3}{16}\)\(⇒\) reciprocal is : \(\frac{16}{x^3}\), 10- A\(f(x) = ln (2x + 1)\)\(y = ln (2x + 1)\)Change variables \(x\) and \(y: x = ln (2y + 1)\)solve: \(x = ln (2y + 1)\)\(y = \frac{e^{x}-1}{2}=\frac{1}{2}(e^{x} – 1)\), Your email address will not be published. "> ���A���>�3�7���Dx����M�>�F��h�7Ut�y�~!G"�*)�J����l=4�#:>09:I�]�A$9���e��v � ���y���;8���z�P�@0�].o��K�y]�V}��ݿ+�1Y�d�$���yQ���� }>����ڏ[�x��}8��֛=1���8��O{t�kV�z=���� for being eligible to sit for this exam include being between the ages of 19 Play as . However, in the MFAT market, the Military Flight Aptitude Test is the best. the Americans with Disabilities Act, be sure to talk to your recruiter about 5- If \(\theta\) is an acute angle and sin \(\theta = \frac{3}{5}\), then cos \(\theta\) =? 5. Which of these is not a criterion for classifying an aircraft? Effortless Math services are waiting for you. Each piece of DNA is described using either A, C, G, or T. Each component is organized in a unique and particular order. The sample math questions you’ll find here are brief samples designed to give you the insights you need to be as prepared as possible for your ASTB Math test. Topics include: Reading Comprehension, Math, Mechanical Comprehension, Nautical Information and Aviation, and much more. Directions: Below are 5 passages each with four possible answer choices. A) C D) Reduce landing weight, A) North Pole Then, you’ll not only find the correct answers, but do it quickly as well. Its been made by Barron’s, one of the tops in the industry and is well organized. Instead, these questions are meant to familiarize examinees with the format and content of questions found within each section. Test takers are assessed on their knowledge of principles related to liquids and gases, as well as their understanding of how liquids and gases affect volume, pressure, and velocity in the Mechanical Comprehension Test of the ASTB. Immediately after completing all seven subtests, you will receive your score report. B) Video conferencing is more economically feasible than traditional face-to-face meetings endobj During the Quiz End of Quiz. The Performance Based Measures Battery will assess your ability to complete listening tasks, answer directional items, and accomplish tracking tasks. A) Documents can be damaged by rust A) 4A + B = 10 The performance of an individual in this examination determines if he/she meets the standards for training. endobj Feedback. Time to Complete: 10 min. Save my name, email, and website in this browser for the next time I comment. © 2020 Study Guide Zone. 1- CMETHOD ONE\(log_4⁡(x+2) – log_4⁡(x-2) = 1\)Add \(log_4⁡(x-2)\) to both sides\(log_4⁡(x+2) – log_4⁡(x-2)+ log_4⁡(x-2)= 1 + log_4⁡(x-2)\)\(log_4⁡(x+2) = 1 + log_4⁡(x-2)\)Apply logarithm rule:\(a = log_b⁡(b^a) ⇒ 1 = log_4⁡(4^1) = log_4⁡(4)\)then: \(log_4⁡(x+2) = log_4⁡(4) + log_4⁡(x-2)\)Logarithm rule: \(log_c⁡(a) + log_c⁡(b) = log_c⁡(ab)\)then: \(log_4⁡(4) + log_4⁡(x-2) = log_4⁡(4(x-2))\)\(log_4⁡(x+2) = log_4⁡(4(x-2))\)When the logs have the same base:\(log_b⁡(f(x)) = log_b⁡(g(x)) ⇒ f(x) = g(x)(x+2) = 4(x-2)\)\(x = \frac{10}{3}\)METHOD TWOWe know that:\(log_a⁡b-log_a⁡c=log_a\frac{b}{c}⁡\space and \space log_a⁡b=c⇒b=a^c\)Then: \(log_4⁡(x+2)- log_4⁡(x-2)=log_4\frac{(x + 2)}{(x – 2)}⁡=1⇒\frac{(x + 2)}{(x – 2)}=4^1=4⇒x+2=4(x-2)⇒x+2=4x-8⇒4x-x=8+2→3x=10⇒x=\frac{10}{3}\), 2- B\(e^{(5x + 1 )}= 10\)If \( f(x) = g(x)\), then \(ln(f(x)) = ln(g(x))\)\(ln⁡(e^{(5x + 1 )})= ln(10)\)Apply logarithm rule:\(log_a⁡(x^b) = b log_a⁡(x)\)\(ln⁡(e^{(5x + 1 )})= (5x + 1)ln(e)\)\((5x + 1)ln(e) = ln(10)\)\((5x + 1)ln(e) = (5x + 1)\)\((5x + 1) = ln(10) \)\( ⇒x = \frac{ln⁡(10) – 1}{5}\), 3- C\(f(x) = x –\frac{5}{3}⇒ y = x – \frac{5}{3}⇒ y+ \frac{5}{3}=x\)\(f^{-1 }= x+ \frac{5}{3}\)\(f ^{–1}(5) = 5 +\frac{5}{3}=\frac{20}{3}\), 4- Ccos \(30^{\circ} = \frac{\sqrt 3}{2}\), 5- Csin\(θ=\frac{3}{5}⇒\) we have following triangle, then:\(c=\sqrt {(5^2-3^2 )}=\sqrt{(25-9)}=\sqrt 16=4\)cos\(θ=\frac{4}{5}\), 6- B\(-2x- y = -9\)\(5x-2y= 18\)\(⇒\) Multiplication \((–2)\) in first equation\(4x +2y =18\)\(5x-2y= 18\)Add two equations together \(⇒ 9x =36 ⇒ x= 4\) then: \(y = 1\), 7- C\(|9 – (12 ÷ | 2 – 5 |)| = |(9-(12÷|-3|))|=|9-(12÷3)|=|9-4|=|5|=5\), 8- DMETHOD ONE\(log_{2}⁡x = 5\)Apply logarithm rule: \(a = log_b⁡(b^a)\)\(5 = log_2⁡(2^5) = log_2⁡(32)\)\(log_2⁡x = log_2⁡(32)\)When the logs have the same base: \(log_b⁡(f(x)) = log_b⁡(g(x))⇒ f(x) = g(x)\)then: \(x = 32\)METHOD TWOWe know that:\(log_a⁡b=c⇒b=a^c \)\(log_2⁡x=5⇒x=2^5=32\), 9- D\(\frac{x^3}{16}\)\(⇒\) reciprocal is : \(\frac{16}{x^3}\), 10- A\(f(x) = ln (2x + 1)\)\(y = ln (2x + 1)\)Change variables \(x\) and \(y: x = ln (2y + 1)\)solve: \(x = ln (2y + 1)\)\(y = \frac{e^{x}-1}{2}=\frac{1}{2}(e^{x} – 1)\), Your email address will not be published. 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astb sample questions


The NATFI is a type of personality test and can’t/shouldn’t be studied for. Questions. <> Quiz Flashcard. _����^t��Pe���Ǖ[�(p��E���-. A) Cyclonic air movement is central in the formation of hurricane force winds By AdewumiKoju | Last updated: May 14, 2019. Difficulty. After this initial stage and through its intermediate stages the storm is called, first, a tropical depression, then it upgrades to a tropical storm and finally, once intensity has increased so much, a hurricane. D) Plastic paper clips never damage documents. ʼ.��](xY �Y1��S�]i{��8�i��'E&����Ihm��x%]�����A�R��eGD��p� }b�o5`ź=��6:hR�U��Bܦ P�c�Dz��2[�mUDI^�,#�PB�ʹ.&���ѓ����y�p��0�ɰ���Pf�#V,lJ(�|�a���(2u<1� [�Z-dQ����j�5����� R{3Ca0&�-��q����A�g�*�+XZ)i�,(�*ڒ��t����{+��("8�y+g8^���[��?��(��-�hW( Meetings will be run in the most economically feasible way. In order to post comments, please make sure JavaScript and Cookies are enabled, and reload the page. The number and focus of the test’s questions will be determined by your answers, and where you are struggling. suitable for pilot and flight officer training programs. The average number of passengers on a bus is 85. The sample items are not meant to provide an exhaustive list of the types of questions that will be found in the test. The fact that this reading comprehension exam is adaptive makes it very different from similar parts of other military flight exams. Please fill out the form below and we will contact you soon. 3- If \(f(x) = x – \frac{5}{3}\) and \(f ^{–1}\) is the inverse of \(f(x)\), what is the value of \(f ^{–1(5)\)? For example, you may see a statement that says, “I sometimes run late for appointments.” You will choose the option of whether or not it describes you. 1. This could include video conferencing or traditional face-to-face meetings. Others have practice tests, which have been proven to increase student scores by a whole letter grade (in some cases more than that)! The Mechanical Comprehension Test will assess physics topics such as gases, liquids, pressure, volume, velocity, engines, electricity, gears, weight distribution, pulleys, and fulcrums. Each time set is appropriate for the exact amount of time per question you’d experience in that section. 3. x��Z�n�8}7��43�E��`���Y�b샳����������~�̿mUQ�H��V��R������^��}����7��e�?��7������O� �n�//���`��Ԭ�*^����"c�����]�&2��I�J�D�����ޤWy���uz���[��Ў^������� �%��H؇*�,e�{z%����J�?�0����P���L���O�MZ��a�.��������fY[t��2wm�K�3�,.��LɊ�� .١������{Ø�����:�B��SϔJG�TS%������?���w�%�6��^u���Hu����R@���C� ��������,�L���|�' �nAy�:��J�g���q�pP@{��l:{I�J��dȌ���0��ڞ�:�����=��h� M�W۱��[������ ħ��=���V���J�dW�I�e���j|&%�k����W$G�� &��w�x3X�ހ���fü(i�;z����9[�֙�wlq �^s�o�� �aKOl|�ڳh抗M���H�Hn�v�\f�{�g�"f� DG��' ��E�ƽ@�����o��۶;�V�J���5zU� ��׋��E$[��R�]�>���A���>�3�7���Dx����M�>�F��h�7Ut�y�~!G"�*)�J����l=4�#:>09:I�]�A$9���e��v � ���y���;8���z�P�@0�].o��K�y]�V}��ݿ+�1Y�d�$���yQ���� }>����ڏ[�x��}8��֛=1���8��O{t�kV�z=���� for being eligible to sit for this exam include being between the ages of 19 Play as . However, in the MFAT market, the Military Flight Aptitude Test is the best. the Americans with Disabilities Act, be sure to talk to your recruiter about 5- If \(\theta\) is an acute angle and sin \(\theta = \frac{3}{5}\), then cos \(\theta\) =? 5. Which of these is not a criterion for classifying an aircraft? Effortless Math services are waiting for you. Each piece of DNA is described using either A, C, G, or T. Each component is organized in a unique and particular order. The sample math questions you’ll find here are brief samples designed to give you the insights you need to be as prepared as possible for your ASTB Math test. Topics include: Reading Comprehension, Math, Mechanical Comprehension, Nautical Information and Aviation, and much more. Directions: Below are 5 passages each with four possible answer choices. A) C D) Reduce landing weight, A) North Pole Then, you’ll not only find the correct answers, but do it quickly as well. Its been made by Barron’s, one of the tops in the industry and is well organized. Instead, these questions are meant to familiarize examinees with the format and content of questions found within each section. Test takers are assessed on their knowledge of principles related to liquids and gases, as well as their understanding of how liquids and gases affect volume, pressure, and velocity in the Mechanical Comprehension Test of the ASTB. Immediately after completing all seven subtests, you will receive your score report. B) Video conferencing is more economically feasible than traditional face-to-face meetings endobj During the Quiz End of Quiz. The Performance Based Measures Battery will assess your ability to complete listening tasks, answer directional items, and accomplish tracking tasks. A) Documents can be damaged by rust A) 4A + B = 10 The performance of an individual in this examination determines if he/she meets the standards for training. endobj Feedback. Time to Complete: 10 min. Save my name, email, and website in this browser for the next time I comment. © 2020 Study Guide Zone. 1- CMETHOD ONE\(log_4⁡(x+2) – log_4⁡(x-2) = 1\)Add \(log_4⁡(x-2)\) to both sides\(log_4⁡(x+2) – log_4⁡(x-2)+ log_4⁡(x-2)= 1 + log_4⁡(x-2)\)\(log_4⁡(x+2) = 1 + log_4⁡(x-2)\)Apply logarithm rule:\(a = log_b⁡(b^a) ⇒ 1 = log_4⁡(4^1) = log_4⁡(4)\)then: \(log_4⁡(x+2) = log_4⁡(4) + log_4⁡(x-2)\)Logarithm rule: \(log_c⁡(a) + log_c⁡(b) = log_c⁡(ab)\)then: \(log_4⁡(4) + log_4⁡(x-2) = log_4⁡(4(x-2))\)\(log_4⁡(x+2) = log_4⁡(4(x-2))\)When the logs have the same base:\(log_b⁡(f(x)) = log_b⁡(g(x)) ⇒ f(x) = g(x)(x+2) = 4(x-2)\)\(x = \frac{10}{3}\)METHOD TWOWe know that:\(log_a⁡b-log_a⁡c=log_a\frac{b}{c}⁡\space and \space log_a⁡b=c⇒b=a^c\)Then: \(log_4⁡(x+2)- log_4⁡(x-2)=log_4\frac{(x + 2)}{(x – 2)}⁡=1⇒\frac{(x + 2)}{(x – 2)}=4^1=4⇒x+2=4(x-2)⇒x+2=4x-8⇒4x-x=8+2→3x=10⇒x=\frac{10}{3}\), 2- B\(e^{(5x + 1 )}= 10\)If \( f(x) = g(x)\), then \(ln(f(x)) = ln(g(x))\)\(ln⁡(e^{(5x + 1 )})= ln(10)\)Apply logarithm rule:\(log_a⁡(x^b) = b log_a⁡(x)\)\(ln⁡(e^{(5x + 1 )})= (5x + 1)ln(e)\)\((5x + 1)ln(e) = ln(10)\)\((5x + 1)ln(e) = (5x + 1)\)\((5x + 1) = ln(10) \)\( ⇒x = \frac{ln⁡(10) – 1}{5}\), 3- C\(f(x) = x –\frac{5}{3}⇒ y = x – \frac{5}{3}⇒ y+ \frac{5}{3}=x\)\(f^{-1 }= x+ \frac{5}{3}\)\(f ^{–1}(5) = 5 +\frac{5}{3}=\frac{20}{3}\), 4- Ccos \(30^{\circ} = \frac{\sqrt 3}{2}\), 5- Csin\(θ=\frac{3}{5}⇒\) we have following triangle, then:\(c=\sqrt {(5^2-3^2 )}=\sqrt{(25-9)}=\sqrt 16=4\)cos\(θ=\frac{4}{5}\), 6- B\(-2x- y = -9\)\(5x-2y= 18\)\(⇒\) Multiplication \((–2)\) in first equation\(4x +2y =18\)\(5x-2y= 18\)Add two equations together \(⇒ 9x =36 ⇒ x= 4\) then: \(y = 1\), 7- C\(|9 – (12 ÷ | 2 – 5 |)| = |(9-(12÷|-3|))|=|9-(12÷3)|=|9-4|=|5|=5\), 8- DMETHOD ONE\(log_{2}⁡x = 5\)Apply logarithm rule: \(a = log_b⁡(b^a)\)\(5 = log_2⁡(2^5) = log_2⁡(32)\)\(log_2⁡x = log_2⁡(32)\)When the logs have the same base: \(log_b⁡(f(x)) = log_b⁡(g(x))⇒ f(x) = g(x)\)then: \(x = 32\)METHOD TWOWe know that:\(log_a⁡b=c⇒b=a^c \)\(log_2⁡x=5⇒x=2^5=32\), 9- D\(\frac{x^3}{16}\)\(⇒\) reciprocal is : \(\frac{16}{x^3}\), 10- A\(f(x) = ln (2x + 1)\)\(y = ln (2x + 1)\)Change variables \(x\) and \(y: x = ln (2y + 1)\)solve: \(x = ln (2y + 1)\)\(y = \frac{e^{x}-1}{2}=\frac{1}{2}(e^{x} – 1)\), Your email address will not be published.

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