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GRE Subject Test: Math : Algebra

Study concepts, example questions & explanations for GRE Subject Test: Math

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Example Questions

Example Question #141 : Algebra

$6^{3}\times6^{n} =6^{12}$

Possible Answers:

n =9

n =15

n=36

n=4

Correct answer:

n =9

Explanation:

$6^{3} \times 6^{n} =6^{12}$

Since the base is for both, then:

3 + n =12 When the base is the same, and you are multiplying, the exponents are added.

n= 9

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Example Question #6 : Solving Exponential Equations

$10^{3x} = 63$

Possible Answers:

$x = \frac{log(63)}{3}$

x = log (63)

x = 63/3

$x = \frac{log (3)}{63}$

Correct answer:

$x = \frac{log(63)}{3}$

Explanation:

$10^{3x} = 63$

To solve, use common $\log$

$\log (10^{3x}) = \log (63)$

$3x\log (10) = \log (63)$

$3x (1) = \log (63)$

$3x = \log (63)$

$x = \frac{\log (63)}{3}$

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Example Question #7 : Solving Exponential Equations

$2^{x} = 40$

Possible Answers:

$x = \ln (40)$

$x = \frac{\\ln ( 40)}{\\ln (2)}$

$x = \frac{\\ln (2) }{\\ ln(40) }$

$x =\frac{\\ln (20)}{\\ln (2)}$

Correct answer:

$x = \frac{\\ln ( 40)}{\\ln (2)}$

Explanation:

$2^{x} = 40$

To solve, use the natural log.

$ln (2^{x}) = ln (40)$

xln (2) = ln(40)

To isolate the variable, divide both sides by ln (2) .

$x = \frac{\\ln (40)}{\\ln (2)}$

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Example Question #8 : Solving Exponential Equations

$4^{x} = 200$

Possible Answers:

$x =\frac{1}{5\\ln }$

$x = \frac{\\ln (4)}{\\ln (200) }$

$x =\frac{\\ln (200)}{\\ln (4) }$

x = 50

Correct answer:

$x =\frac{\\ln (200)}{\\ln (4) }$

Explanation:

$4^{x} = 200$

To solve, use the natural log.

$\\ln (4^{x}) = \ln(200)$

$x\ln (4) = \ln (200)$

$x = \ln (200)$

$x = \frac{ln(200)}{ln (4)}$

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Example Question #9 : Solving Exponential Equations

Solve the equation. Express the solution as a logarithm in base-10.

$-2\times 10^{3x} = - 500$

Possible Answers:

$x = \log (250)$

$x =\frac{\log500 }{3}$

$x=\frac{\log (250)}{3}$

$x = \frac{\log 3}{250}$

Correct answer:

$x=\frac{\log (250)}{3}$

Explanation:

$-2 (10^{3x}) = -500$

Isolate the exponential part of the equation.

$\frac{-2 (10^{3x})}{-2} = \frac{-500}{-2}$

$10^{3x} = 250$

Convert to log form and solve.

$\log_{10} (250) = 3x$

$\log_{10} (250)$ can also be written as $\log 250$ .

$\frac{\log (250) }{3} = x$

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Example Question #142 : Algebra

$8\times e^{0.3x} = 12$

Possible Answers:

$\frac{\\ln (12)}{0.3} = x$

$\frac{\\ln 0.3}{12} = x$

$\frac{\\ln (1.5)}{0.3} = x$

$\frac{\\ln (8)}{0.3} = x$

Correct answer:

$\frac{\\ln (1.5)}{0.3} = x$

Explanation:

$8\times e^{0.3x} = 12$

Simply the exponential part of the equation by dividing both sides by

$e^{0.3x} = \frac{12}{8}$

$e^{0.3x} = 1.5$

Write in logarithm form.

$\log_{e} (1.5) = 0.3x$

Because $\log_{e} (1.5)$ is also written as $\\ln 1.5$

$\frac{\\ln 1.5}{0.3} = x$

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Example Question #143 : Algebra

Solve this exponential equation for

$6\times e^{0.1x} = 72$

Possible Answers:

$x = 10 \times\ln (12)$

$x = 10 \times 72\ln$

$x = 12\ln$

$x = 10 \times \ln (6)$

Correct answer:

$x = 10 \times\ln (12)$

Explanation:

$6\times e ^{0.1x} = 72$

Isolate the variable by dividing by 6.

$e ^{0.1x} = 12$

$\log_{e} (12) =0.1x$

$\log_{e} (12)$ is the same as $\ln (12)$ .

$\frac{\ln(12)}{0.1} = x$

$x = 10 \times \ln (12)$

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Example Question #144 : Algebra

$10^{x+3} - 7 = 50$

Possible Answers:

$x = \log (57) -3$

$x = \log (3) -50$

$x = \log (57)$

$x = \log (57) + 3$

Correct answer:

$x = \log (57) -3$

Explanation:

$10^{^{x+3}} - 7 = 50$

Isolate by adding to both sides of the exponential equation.

$10^{^{x+3}} = 57$

Take the common log.

$\log (10^{x+3}) = \log (57)$

Use logarithmic rule 3. An exponent inside a log can be moved outside as a multiplier.

$(x+3) \log (10) = \log (57)$

Simplify. Because $\log (10) = 1$

$(x + 3) = \log (57)$

Isolate the variable by subtracting from both sides.

$x = \log (57) -3$

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Example Question #145 : Algebra

$\frac{3000}{2 + 7^{2x}} = 5$

Possible Answers:

$x = \frac{\log_{7}(602)}{2}$

$x = \log_{7}(598)$

$x = \frac{\log_{7}(598)}{2}$

$x = \frac{\log_{7}(600)}{2}$

Correct answer:

$x = \frac{\log_{7}(598)}{2}$

Explanation:

$\frac{3000}{2 + 7^{2x}} = 5$

$3000 = 5 (7^{2x} +2)$

Simplify by dividing both sides by

$600 = 7^{2x} +2$

Subtract from both sides of the exponential equation.

$598 = 7^{2x}$

Since base is 7, take log 7 of both sides.

$\log_{7} (7^{2x}) =\log_{7} (598)$

Use logarithmic rule 3. An exponent on everything inside a log can be moved out front as a multiplier,

$2x (\log_{7})7 = \log_{7} (598)$

$\log_{7} \times 7 =1$

$2x = \log_{7} (598)$

Simplify by dividing both sides of the exponential equation by 2.

$x = \frac{\log_{7} (598)}{2}$

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Example Question #146 : Algebra

$2 (2^{x+3}) =355$

Possible Answers:

$x = \frac{\ln {3}}{\ln (2)} - 3$

$x = \frac{\ln \frac{355}{2}}{\ln (2)} - 3$

$x = \frac{\ln \frac{355}{3}}{\ln (2)} + 3$

$x = \frac{\ln{355}}{\ln (2)} - 3$

Correct answer:

$x = \frac{\ln \frac{355}{2}}{\ln (2)} - 3$

Explanation:

$2 (2^{x+3}) =355$

To solve, use the natural $\log$ .

$\ln (2^{x+3}) =\ln (355/2)$

$(x+3) (\ln )(2) = \ln \frac{355}{2}$

$x + 3= \frac{\ln \frac{355}{2}}{\ln (2)}$

$x = \frac{\ln \frac{355}{2}}{\ln (2)} - 3$

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GRE Subject Test: Math : Algebra

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #141 : Algebra

Example Question #6 : Solving Exponential Equations

Example Question #7 : Solving Exponential Equations

Example Question #8 : Solving Exponential Equations

Example Question #9 : Solving Exponential Equations

Example Question #142 : Algebra

Example Question #143 : Algebra

Example Question #144 : Algebra

Example Question #145 : Algebra

Example Question #146 : Algebra

All GRE Subject Test: Math Resources

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