PSAT Math : How to find a ratio of exponents

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #2 : How To Find A Ratio Of Exponents

If \(\displaystyle m\) and \(\displaystyle n\) are positive integers and \(\displaystyle 4^m=64^n\), then what is the value of \(\displaystyle \frac{m}{n}\)?

Possible Answers:

\(\displaystyle 3\)

\(\displaystyle \frac{5}{3}\)

\(\displaystyle \frac{1}{16}\)

\(\displaystyle \frac{1}{3}\)

\(\displaystyle 16\)

Correct answer:

\(\displaystyle 3\)

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 #3 : How To Find A Ratio Of Exponents

Write the following logarithm in expanded form:

 

\(\displaystyle \log x^{2}y\)

Possible Answers:

\(\displaystyle 2\log x-\log y\)

\(\displaystyle \log x+\log y\)

\(\displaystyle 2\log x+\log y\)

\(\displaystyle 2\left ( \log xy \right )\)

\(\displaystyle \log x^{2}+\log y\)

Correct answer:

\(\displaystyle 2\log x+\log y\)

Explanation:

\(\displaystyle \log x^{2}y=\log x^{2}+\log y=2\log x+\log y\)

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