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GRE Subject Test: Math : Evaluating Logarithms

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Example Questions

Example Question #1 : Logarithms

Solve: $\displaystyle log_4 256=x$

Possible Answers:

x=10 $\displaystyle x=10$

x=6 $\displaystyle x=6$

x=4 $\displaystyle x=4$

x=-4 $\displaystyle x=-4$

Correct answer:

x=4 $\displaystyle x=4$

Explanation:

Step 1: Re-write the log equation as an exponential equation. To do this, take the base of the log function and raise it to the number on the right side of the equal sign. This new exponent is equal to the number to the right of the log base.

4^x=256 $\displaystyle 4^x=256$

Step 2: Re-write the right hand side as a power of 4..

256=4^4 $\displaystyle 256=4^4$

Step 3: Re-write the equation

4^x=4^4 $\displaystyle 4^x=4^4$

Step 4: We have the same base, so we can equal the exponents..

x=4 $\displaystyle x=4$

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Example Question #1 : Logarithms

$Solve\ for\ x: log_{x}(49)=2$ $\displaystyle Solve\ for\ x: log_{x}(49)=2$

Possible Answers:

24.5 $\displaystyle 24.5$

$\displaystyle 98$

$\pm7$ $\displaystyle \pm7$

49^2 $\displaystyle 49^2$

Correct answer:

$\pm7$ $\displaystyle \pm7$

Explanation:

In order to solve for x, we must first rewrite the log in exponential form.

Every log is written in the below general form:

$log_{base}(result)=exponent\ is\ rewritten\ as: base^e^x^p^o^n^e^n^t=result$

In this case we have:

$log_{x}(49)=2$ $\displaystyle log_{x}(49)=2$

This becomes:

x^2=49 $\displaystyle x^2=49$

We can solve this by taking the square root of both sides:

$\sqrt{x^2}=\sqrt{49}$ $\displaystyle \sqrt{x^2}=\sqrt{49}$

$x=\pm7$ $\displaystyle x=\pm7$

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Example Question #1 : Logarithms

Solve for $\displaystyle x$ :

$\displaystyle log_4 4096=x$

Possible Answers:

x=9 $\displaystyle x=9$

x=4 $\displaystyle x=4$

x=2 $\displaystyle x=2$

x=7 $\displaystyle x=7$

x=6 $\displaystyle x=6$

Correct answer:

x=6 $\displaystyle x=6$

Explanation:

Use rules of logarithms...

Take the base of the log and raise it to the number on the right side of the equal sign (which becomes the exponent):

$\displaystyle 4^x=4096$

$\\4^x=16^3 \\4^x=(4^2)^3 \\4^x=4^6 \\x=6$ $\displaystyle \\4^x=16^3 \\4^x=(4^2)^3 \\4^x=4^6 \\x=6$

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Example Question #1 : Logarithms

Evaluate: $\log_6 46656=x$ $\displaystyle \log_6 46656=x$

Possible Answers:

$\displaystyle 4$

$\displaystyle 6$

$\displaystyle 5$

$\displaystyle 8$

Correct answer:

$\displaystyle 6$

Explanation:

Step 1: Write the expression in exponential form...

Given: $\log_a b=x\implies a^x=b$ $\displaystyle \log_a b=x\implies a^x=b$

$\log_6 46656=x\implies 6^x=46656$

Step 2: Convert the right hand side into a power of 6..

$\displaystyle 46656=6^6$

Step 3: Re-write the equations...

6^x=6^6 $\displaystyle 6^x=6^6$

Since the bases are equal, taking log of both sides will cancel them.

$\log_6 6^x=\log_6 6^6$ $\displaystyle \log_6 6^x=\log_6 6^6$

$\implies x=6$ $\displaystyle \implies x=6$

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Example Question #1 : Evaluating Logarithms

$Solve\ for\ x:\ log_{2}(8)=x$ $\displaystyle Solve\ for\ x:\ log_{2}(8)=x$

Possible Answers:

$\displaystyle 2$

$\displaystyle 3$

$\displaystyle 6$

$\displaystyle 4$

Correct answer:

$\displaystyle 3$

Explanation:

$In\ order\ to\ solve\ for\ x\ we\ must\ know\ how\ to\ rewrite\ a\ log\ in\ exponent\ form:$ $\displaystyle In\ order\ to\ solve\ for\ x\ we\ must\ know\ how\ to\ rewrite\ a\ log\ in\ exponent\ form:$

$We\ can\ use\ the\ general\ rule:\ log_{b}(a)=x\\ when\ rewritten\ in\ exponential\ form\ we\ get: b^{x}=a$ $\displaystyle We\ can\ use\ the\ general\ rule:\ log_{b}(a)=x\\ when\ rewritten\ in\ exponential\ form\ we\ get: b^{x}=a$

$To\ Solve\ for\ x:\ log_{2}(8)=x;\ we\ rewrite\ as\ 2^{x}=8$ $\displaystyle To\ Solve\ for\ x:\ log_{2}(8)=x;\ we\ rewrite\ as\ 2^{x}=8$

$We\ know\ that\ 2^{3}=8;\ so\ the\ value\ of\ x=3$ $\displaystyle We\ know\ that\ 2^{3}=8;\ so\ the\ value\ of\ x=3$

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GRE Subject Test: Math : Evaluating Logarithms

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

All GRE Subject Test: Math Resources

Example Questions

Example Question #1 : Logarithms

Example Question #1 : Logarithms

Example Question #1 : Logarithms

Example Question #1 : Logarithms

Example Question #1 : Evaluating Logarithms

All GRE Subject Test: Math Resources

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