# PSAT Math : Exponential Ratios and Rational Numbers

## Example Questions

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### Example Question #531 : Algebra

If  and are positive integers and , then what is the value of ?

Explanation:

43 = 64

Alternatively written, this is 4(4)(4) = 64 or 43 = 641.

Thus, m = 3 and n = 1.

m/n = 3/1 = 3.

### Example Question #1 : How To Find A Ratio Of Exponents

Write the following logarithm in expanded form:

Explanation:

### Example Question #231 : Exponents

Which of the following lists the above quantities from least to greatest?

II, III, I, IV

I, III, II, IV

IV, III, II, I

I, IV, II, III

I, IV, III, II

I, III, II, IV

Explanation:

Solve for .

Explanation:

Since

Hence

Simplify:

Explanation:

### Example Question #3 : Exponents And Rational Numbers

Solve for :

Explanation:

From the equation one can see that

Hence  must be equal to 25.

Evaluate:

Explanation:

Solve for .

Explanation:

### Example Question #1 : Exponents And Rational Numbers

and

Find

Explanation:

Hence the correct answer is .

### Example Question #1 : How To Find An Exponent From A Rational Number

Solve for .

Explanation:

Use the rules of logarithms to combine terms.

Hence,

By fatoring we get

Hence .

However, you cannot take the logarithm of a negative number. Thus, the only value for is .

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