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GRE Subject Test: Math : Change of Base

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

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Example Questions

Example Question #1 : Change Of Base

Evaluate:

$3^{3x+3}=27^{2x+2}$

Possible Answers:

$\frac{2}{3}$

$\frac{4}{13}$

$\frac{1}{2}$

$-\frac{1}{2}$

Correct answer:

Explanation:

In order to evaluate the unknown variable, it is necessary to change the base. Looking at the right side of the equation, 27 is equivalent to three cubed.

3^3=27

Therefore, converting the right side of the equation to a base of 3 will allow setting both the left and right side of the exponential terms equal to each other.

$3^{3x+3}=27^{2x+2}$

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

Log both sides to drop the exponents by log properties, and divide the log based 3 on both sides to cancel this term.

Solve for x.

$ln\: 3^(^3^x^+^3^)=ln\:3^3^(^2^x^+^2^)$

3x+3=3(2x+2)

3x+3=6x+6

-3=3x

x=-1

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Example Question #2 : Change Of Base

Evaluate the following logarithm:

$log_{377}(563)$

Possible Answers:

1.068

1.238

4.652

0.937

0.982

Correct answer:

1.068

Explanation:

The simplest way to evaluate a logarithm that doesn't have base 10 is with change of base formula:

$log_ba=\frac{log_ca}{log_cb}$

So we have

$log_{377}(563)$

$log_{377}563=\frac{log_{10}563}{log_{10}377}\approx1.068$

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Example Question #3 : Change Of Base

$Solve\ for\ x: 3^x=23$

Possible Answers:

2.85405

2.73058

1.89205

1.683099

Correct answer:

2.85405

Explanation:

In order to solve a logarithm, we must first rewrite it in log form:

$3^x=23\ written\ in\ log\ form\ is: log_{3}(23)=x$

To solve for x, we must use the Change of Base:

$log_{3}(23)=\frac{log(23)}{log(3)}$

$\frac{log(23)}{log(3)}=2.85405$

This means that:

$3^{2.85405}=23$

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GRE Subject Test: Math : Change of Base

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

All GRE Subject Test: Math Resources

Example Questions

Example Question #1 : Change Of Base

Example Question #2 : Change Of Base

Example Question #3 : Change Of Base

All GRE Subject Test: Math Resources

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