GRE Subject Test: Math : Logarithmic Properties

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

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Example Questions

Example Question #1 : Logarithmic Properties

Rewrite the following expression as a single logarithm

Possible Answers:

Correct answer:

Explanation:

Recall a few properties of logarithms:

1.When adding logarithms of like base, we multiply the inside.

2.When subtracting logarithms of like base, we divide the inside.

3. When multiplying a logarithm by a number, we can raise the inside to that power.

So we begin with this:

I would start with 3 to simplify the first log.

Next, use rule 1 on the first two logs.

Then, use rule 2 to combine these two.

So our answer is 6.06.

Example Question #2 : Logarithmic Properties

Possible Answers:

Correct answer:

Explanation:

When combining logarithms into one log, we must remember that addition and multiplication are linked and subtraction and division are linked. 

In this case we have multiplication and division - so we assume anything that is negative, must be placed in the bottom of the fraction. 

 

 

Example Question #3 : Logarithmic Properties

Possible Answers:

Correct answer:

Explanation:

When rewriting an exponential function as a log, we must follow the model below: 

A log is used to find an exponent. The above corresponds to the exponential form below: 

Example Question #4 : Logarithmic Properties

Possible Answers:

Correct answer:

Explanation:

In order to rewrite a log, we must remember the pattern that they follow below: 

In this question we have: 

 

Example Question #5 : Logarithmic Properties

Express  as a single logarithm. 

Possible Answers:

Correct answer:

Explanation:

Step 1: Recall all logarithm rules:

Step 2: Rewrite the first term in the expression..

Step 3: Re-write the third term in the expression..

Step 4: Add up the positive terms...

Step 5: Subtract the answer the other term from the answer in Step 4.

Example Question #6 : Logarithmic Properties

Possible Answers:

Correct answer:

Explanation:

In order to expand this log, we must remember the log rules. 

Example Question #7 : Logarithmic Properties

Possible Answers:

Correct answer:

Explanation:

 

Example Question #8 : Logarithmic Properties

Possible Answers:

Correct answer:

Explanation:

Example Question #9 : Logarithmic Properties

Rewrite the following expression as a single logarithm

Possible Answers:

Correct answer:

Explanation:

Recall a few properties of logarithms:

1.When adding logarithms of like base, we multiply the inside.

2.When subtracting logarithms of like base, we divide the inside.

3. When multiplying a logarithm by a number, we can raise the inside to that power.

So we begin with this:

I would start with 3 to simplify the first log.

Next, use rule 1 on the first two logs.

Then, use rule 2 to combine these two.

So our answer is 6.06.

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