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GRE Subject Test: Math : Exponential Functions

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Example Question #11 : Solving Exponential Equations

Solve this exponential equation for

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

Possible Answers:

$x = 12\ln$

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

$x = 10 \times 72\ln$

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

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 #331 : Gre Subject Test: Math

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

Possible Answers:

$x = \log (57) + 3$

$x = \log (57) -3$

$x = \log (3) -50$

$x = \log (57)$

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 #11 : Exponential Functions

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

Possible Answers:

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

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

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

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

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 #11 : Exponential Functions

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

Possible Answers:

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

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

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

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

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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Example Question #11 : Solving Exponential Equations

$6 \times 3^{2y} = 216$

Possible Answers:

$y=\log_{36} (3)$

$y=\frac{\log_{36}(3)}{6}$

$y =\log_{3} (36)$

$y=\frac{\log_{3}(36)}{2}$

Correct answer:

$y=\frac{\log_{3}(36)}{2}$

Explanation:

$6 \times 3^{2y} = 216$

Divide both sides by

$3^{2y} = 36$

Write in logarithm form and solve for

$2y =\log_{3} (36)$

Divide both sides by

$y = \frac{\log_{e} (36)}{2}$

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Example Question #11 : Solving Exponential Equations

$10 \times 3^{\frac{3t}{4}} = 200$

Possible Answers:

$\frac{3}{4} \times \frac{\\\log {20}}{\log{3}} = t$

$\frac{3}{4} \times \frac{\\\\log{3}}{\log{20}}$

$\frac{4}{3} \times \frac{\\\log {20}}{\log{3}} = t$

$\frac{4}{3} \times \frac{\\\\log{3}}{\log{20}} = t$

Correct answer:

$\frac{4}{3} \times \frac{\\\log {20}}{\log{3}} = t$

Explanation:

$10 \times 3^{\frac{3t}{4}} = 200$

Isolate the variable by dividing both sides of the equation by 10.

$3^{\frac{3t}{4}} = 20$

Write in logarithm form.

$\log_{3}= (20)\frac{3^{t}}{4}$

$\frac{4}{3}\log_{3} (20) = t$

Because the solution is in base-3 log, it can be changed to base -10 by using:

$\log_{b} (a) = \frac{\log_{x}(a)}{\log_{x}(b)}$

$\frac{4}{3}\log_{3} (20) = t$

$\frac{4}{3} \times \frac{\\\log {20}}{\log{3}} = t$

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Example Question #151 : Algebra

Solve for x: $2^{x+1}=128$

Possible Answers:

x=6

x=5

x=10

x=7

Correct answer:

x=6

Explanation:

Step 1: Rewrite the right side of the equation into a power of 2.

$128=2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2=2^7$

$2^{x+1}=2^7$

Step 2: We have the same base, so we can equate the exponents.

x+1=7

Step 3: Solve for x. We will subtract 1 from both sides to isolate x.

x+1-1=7-1
$\rightarrow x=6$

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Example Question #18 : Solving Exponential Equations

Solve for :

$2^{x^2-3x}=4^{5}$

Possible Answers:

x=-5, x=2

x=5, x=-2

x=-2

x=-5

Correct answer:

x=5, x=-2

Explanation:

Step 1: Rewrite 4^5 as 2^n .

$4^5 \equiv 2^{10}$

n=10

Step 2: Re-write the equation:

$2^{x^2-3x}=2^{10}$

Step 3: By laws of exponents, if the bases are the same, we can equate the exponents...

We will get x^2-3x=10

Step 4: Move 10 over and begin factoring:

x^2-3x-10=0
(x-5)(x+2)=0
x=5, x=-2

Step 5: x=-2 is a correct answer... we can plug it in and see:

$2^{(-2)^2-3(-2)}=2^{4--6}=2^{10}$

Step 6: x=5 is the other correct answer...

$2^{(5)^2-3(5)}=2^{25-15}=2^{10}$

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Example Question #11 : Exponential Functions

Solve: 2^x=4^3

Possible Answers:

x=2

x=4

x=6

x=9

Correct answer:

x=6

Explanation:

Step 1: Rewrite the right hand side of the equation as a power of 2.

$4^3\equiv 2^6$ . To get this, divide the base by 2 and multiply that 2 to the exponent...

Step 2: Equate the left and right side together

2^x=2^6

We have the same base, so we equate the exponents together..

x=6 ...

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Example Question #12 : Solving Exponential Equations

Solve for :

2^x=8^3

Possible Answers:

x=10

x=8

$x=\frac {1}{9}$

x=9

Correct answer:

x=9

Explanation:

Step 1: Write 8^3 as 2^n ...

$8\cdot8\cdot8=(2\cdot 2\cdot 2)(2\cdot 2\cdot 2)(2\cdot 2\cdot 2)=2^9$

Step 2: Rewrite 8^3 as 2^9 in the original equation..

2^n=2^9

Step 3: By a rule of exponents, I can set the exponents equal if the bases of both exponents are the same...

So, n=9

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GRE Subject Test: Math : Exponential Functions

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

All GRE Subject Test: Math Resources

Example Questions

Example Question #11 : Solving Exponential Equations

Example Question #331 : Gre Subject Test: Math

Example Question #11 : Exponential Functions

Example Question #11 : Exponential Functions

Example Question #11 : Solving Exponential Equations

Example Question #11 : Solving Exponential Equations

Example Question #151 : Algebra

Example Question #18 : Solving Exponential Equations

Example Question #11 : Exponential Functions

Example Question #12 : Solving Exponential Equations

All GRE Subject Test: Math Resources

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