# GRE Subject Test: Math : Logarithmic Properties

## Example Questions

### Example Question #1 : Logarithmic Properties

Rewrite the following expression as a single logarithm

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:

Next, use rule 1 on the first two logs.

Then, use rule 2 to combine these two.

### Example Question #3 : Logarithms

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 #1 : Logarithmic Properties

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 #2 : Logarithmic Properties

Explanation:

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

In this question we have:

### Example Question #6 : Logarithms

Express  as a single logarithm.

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 #4 : Logarithmic Properties

Explanation:

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

Explanation:

Explanation:

### Example Question #7 : Logarithmic Properties

Rewrite the following expression as a single logarithm

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: