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SAT Math : How to find a ratio of exponents

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Example Question #1 : 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 $\frac{m}{n}$ $\displaystyle \frac{m}{n}$?

Possible Answers:

$\frac{5}{3}$ $\displaystyle \frac{5}{3}$

$\displaystyle 16$

$\displaystyle 3$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\frac{1}{16}$ $\displaystyle \frac{1}{16}$

Correct answer:

$\displaystyle 3$

Explanation:

4³= 64

Alternatively written, this is 4(4)(4) = 64 or 4³= 64^1.

Thus, m = 3 and n = 1.

m/n = 3/1 = 3.

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Example Question #115 : Exponents

Write the following logarithm in expanded form:

$\log x^{2}y$ $\displaystyle \log x^{2}y$

Possible Answers:

$2\log x-\log y$ $\displaystyle 2\log x-\log y$

$\log x^{2}+\log y$ $\displaystyle \log x^{2}+\log y$

$2\log x+\log y$ $\displaystyle 2\log x+\log y$

$\log x+\log y$ $\displaystyle \log x+\log y$

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

Correct answer:

$2\log x+\log y$ $\displaystyle 2\log x+\log y$

Explanation:

$\log x^{2}y=\log x^{2}+\log y=2\log x+\log y$ $\displaystyle \log x^{2}y=\log x^{2}+\log y=2\log x+\log y$

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Example Question #22 : Exponents

If $\displaystyle m$ and $\displaystyle n$ are both rational numbers and $4^{m} = 8^{n}$ $\displaystyle 4^{m} = 8^{n}$, what is $\frac{m}{n}$ $\displaystyle \frac{m}{n}$?

Possible Answers:

$\frac{2}{1}$ $\displaystyle \frac{2}{1}$

$\frac{5}{3}$ $\displaystyle \frac{5}{3}$

$\frac{4}{1}$ $\displaystyle \frac{4}{1}$

$\frac{3}{2}$ $\displaystyle \frac{3}{2}$

Correct answer:

$\frac{3}{2}$ $\displaystyle \frac{3}{2}$

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.

$4^{1} = 4, 4^{2} = 16, 4^{3} = 64, 4^{4} = 256, 4^{5} = 1024$ $\displaystyle 4^{1} = 4, 4^{2} = 16, 4^{3} = 64, 4^{4} = 256, 4^{5} = 1024$

$8^{1}=8, 8^{2} = 64, 8^{3} = 512, 8^{4} = 4096, 8^{5} = 32768$ $\displaystyle 8^{1}=8, 8^{2} = 64, 8^{3} = 512, 8^{4} = 4096, 8^{5} = 32768$

And, would you look at that. $4^{3}= 8^{2}$ $\displaystyle 4^{3}= 8^{2}$. Therefore, $\frac{m}{n} = \frac{3}{2}$ $\displaystyle \frac{m}{n} = \frac{3}{2}$.

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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

Example Question #115 : Exponents

Example Question #22 : Exponents

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