# GRE Subject Test: Math : Solving Exponential Equations

## Example Questions

### Example Question #1 : Solving Exponential Equations

Find one possible value of , given the following equation:

Cannot be determined from the information given.

Explanation:

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 .

Explanation:

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 #131 : Algebra

Solve for

Explanation:

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 #131 : Classifying Algebraic Functions

Solve for

Explanation:

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

Explanation:

Since the base is  for both, then:

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

### Example Question #1 : Solving Exponential Equations

Explanation:

To solve, use common

### Example Question #1 : Exponential Functions

Explanation:

To solve, use the natural log.

To isolate the variable, divide both sides by .

### Example Question #1 : Solving Exponential Equations

Explanation:

To solve, use the natural log.

### Example Question #1 : Solving Exponential Equations

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

Explanation:

Isolate the exponential part of the equation.

Convert to log form and solve.

can also be written as .