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

Solve for .       Explanation:

Since Hence ### Example Question #2 : Exponents And Rational Numbers

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.

### Example Question #4 : Exponents And Rational Numbers

Evaluate:       Explanation:  ### Example Question #5 : Exponents And Rational Numbers

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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