How to find a ratio of exponents

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SAT Math › How to find a ratio of exponents

Questions 1 - 3

1

If and are positive integers and , then what is the value of $\frac{m}{n}$ ?

$\frac{1}{16}$

$\frac{1}{3}$

$\frac{5}{3}$

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.

2

Write the following logarithm in expanded form:

$\log x^{2}y$

$2\log x+\log y$

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

$2\log x-\log y$

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

$\log x+\log y$

Explanation

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

3

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

$\frac{3}{2}$

$\frac{2}{1}$

$\frac{4}{1}$

$\frac{5}{3}$

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.

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

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

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

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