SAT Math : How to find a ratio of exponents

Study concepts, example questions & explanations for SAT Math

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Example Questions

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

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

Possible Answers:

Correct answer:

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 #2304 : Act Math

Write the following logarithm in expanded form:

 

Possible Answers:

Correct answer:

Explanation:

Example Question #572 : Algebra

If  and  are both rational numbers and , what is ?

Possible Answers:

Correct answer:

Explanation:

This question is asking you for the ratio of m to n.  To figure it out, the easiest way is to figure out when 4 to an exponent equals 8 to an exponent.  The easiest way to do that is to list the first few results of 4 to an exponent and 8 to an exponent and check to see if any match up, before resorting to more drastic means of finding a formula.

And, would you look at that. .  Therefore, .

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