### All GRE Subject Test: Math Resources

## Example Questions

### Example Question #1 : Exponential Functions

Find one possible value of , given the following equation:

**Possible Answers:**

Cannot be determined from the information given.

**Correct answer:**

We begin with the following:

This can be rewritten as

Recall that if you have two exponents with equal bases, you can simply set the exponents equal to eachother. Do so to get the following:

Solve this to get t.

### Example Question #1 : Exponential Functions

Solve for .

**Possible Answers:**

**Correct answer:**

We need to make the bases equal before attempting to solve for . Since we can rewrite our equation as

** Remember**: the exponent rule

Now that our bases are equal, we can set the exponents equal to each other and solve for .

### Example Question #1 : Solving Exponential Equations

Solve for .

**Possible Answers:**

**Correct answer:**

The first step is to make sure we don't have a zero on one side which we can easily take care of:

Now we can take the logarithm of both sides using natural log:

**Note:** we can apply the Power Rule here

### Example Question #2 : Exponential Functions

Solve for .

**Possible Answers:**

**Correct answer:**

Before beginning to solve for , we need to have a coefficient of :

Now we can take the natural log of both sides:

**Note:**

### Example Question #1 : Exponential Functions

**Possible Answers:**

**Correct answer:**

Since the base is for both, then:

When the base is the same, and you are multiplying, the exponents are added.

### Example Question #1 : Exponential Functions

**Possible Answers:**

**Correct answer:**

To solve, use common

### Example Question #4 : Exponential Functions

**Possible Answers:**

**Correct answer:**

To solve, use the natural log.

To isolate the variable, divide both sides by .

### Example Question #5 : Exponential Functions

**Possible Answers:**

**Correct answer:**

To solve, use the natural log.

### Example Question #6 : Exponential Functions

Solve the equation. Express the solution as a logarithm in base-10.

**Possible Answers:**

**Correct answer:**

Isolate the exponential part of the equation.

Convert to log form and solve.

can also be written as .

### Example Question #1 : Exponential Functions

**Possible Answers:**

**Correct answer:**

Simply the exponential part of the equation by dividing both sides by

Write in logarithm form.

Because is also written as

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