### All GRE Subject Test: Math Resources

## Example Questions

### Example Question #1 : Logarithms

Rewrite the following expression as a single logarithm

**Possible Answers:**

**Correct answer:**

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 #7 : Logarithms

**Possible Answers:**

**Correct answer:**

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 #8 : Logarithms

**Possible Answers:**

**Correct answer:**

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 #9 : Logarithms

**Possible Answers:**

**Correct answer:**

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

In this question we have:

### Example Question #2 : Logarithms

Express as a single logarithm.

**Possible Answers:**

**Correct answer:**

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 #1 : Logarithmic Properties

**Possible Answers:**

**Correct answer:**

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

### Example Question #2 : Logarithmic Properties

**Possible Answers:**

**Correct answer:**

### Example Question #3 : Logarithmic Properties

**Possible Answers:**

**Correct answer:**

### Example Question #4 : Logarithmic Properties

Rewrite the following expression as a single logarithm

**Possible Answers:**

**Correct answer:**

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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