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GRE Subject Test: Math : Evaluating Logarithms

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

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Example Questions

Example Question #1 : Evaluating Logarithms

Solve: log_4 256=x

Possible Answers:

x=-4

x=10

x=6

x=4

Correct answer:

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

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

256=4^4

Step 3: Re-write the equation

4^x=4^4

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

x=4

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Example Question #1 : Logarithms

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

Possible Answers:

$\pm7$

49^2

24.5

Correct answer:

$\pm7$

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:

$log_{x}(49)=2$

This becomes:

x^2=49

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

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

$x=\pm7$

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Example Question #2 : Logarithms

Solve for :

log_4 4096=x

Possible Answers:

x=7

x=4

x=9

x=2

x=6

Correct answer:

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):

4^x=4096

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

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Example Question #1 : Logarithms

Evaluate: $\log_6 46656=x$

Possible Answers:

Correct answer:

Explanation:

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

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

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

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

46656=6^6

Step 3: Re-write the equations...

6^x=6^6

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

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

$\implies x=6$

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Example Question #4 : Logarithms

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

Possible Answers:

Correct answer:

Explanation:

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

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

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

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

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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 : Evaluating Logarithms

Example Question #1 : Logarithms

Example Question #2 : Logarithms

Example Question #1 : Logarithms

Example Question #4 : Logarithms

All GRE Subject Test: Math Resources

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