## Example Questions

### Example Question #2351 : Act Math

Which of the following is a value of that satisfies ?      Explanation:

When you have a logarithm in the form ,

it is equal to .

Using the information given, we can rewrite the given equation in the second form to get .

Now solving for we get the result. ### Example Question #2351 : Act Math

Solve for :       Explanation:

When you have a logarithm in the form ,

it is equal to .

We can rewrite the given equation as Solving for , we get  .

### Example Question #3 : How To Find A Rational Number From An Exponent

Solve for :       Explanation:

When you have a logarithm in the form ,

it is equal to .

We can rewrite the given equation as Solving for , we get .

### Example Question #171 : Exponents

Converting exponents to rational numbers often allows for faster simplification of those numbers.

Which of the following is incorrect? Convert exponents to rational numbers.      Explanation:

To identify which answer is incorrect we need to do each of the conversions.

First lets look at   .

Therefore this conversion is true.

Next lets look at . For this particular one we can recognize that anything raised to a zero power is just one therefore this conversion is true.

From here lets look at    Thus . Therefore this is an incorrect conversion and thus our answer.

### Example Question #5 : How To Find A Rational Number From An Exponent

Sometimes, seeing rational numbers makes it easier to understand an equation.

Convert the following into a rational number or numbers:       Explanation:

The rule for converting exponents to rational numbers is: .

Even with this, it is easier to work the problem as far as we can with exponents, then switch to rational expression when we run out of room: At last, we convert, and obtain .

Thus, .

### All ACT Math Resources 