# GRE Subject Test: Math : Solving Exponential Equations

## Example Questions

### Example Question #21 : Solving Exponential Equations

Solve for

Explanation:

Step 1: Rewrite the right side as a power of :

Step 2: Rewrite the original equation:

Step 3: Since the bases are equal, I can set the exponents equal.

So,

### Example Question #341 : Gre Subject Test: Math

Solve for

Explanation:

Rewrite the right hand side such that it has the same base as the expression on the right hand side.

Apply the rule of stacked exponents. We multiply the exponents together and keep the same base:

Now that we have rewrote the right hand side in the same way as the left, we can equate them:

Now that we have the same bases, we can equal the exponents and solve for x...

### Example Question #21 : Solving Exponential Equations

Find the value  that makes the statement  true.

Explanation:

Step 1: Re-write the left side so we have the same base as the right side...

Step 2: Multiply the stacked exponents on the left hand side...

We will apply the rule:

So,

Step 3: We can now set the exponents equal to each other, since we have the same base.

### Example Question #21 : Solving Exponential Equations

Find one possible value of , given the following equation:

Cannot be determined from the information given.