1950 AHSME Problems/Problem 25

Problem

The value of $\log_{5}\frac{(125)(625)}{25}$ is equal to:

$\textbf{(A)}\ 725\qquad\textbf{(B)}\ 6\qquad\textbf{(C)}\ 3125\qquad\textbf{(D)}\ 5\qquad\textbf{(E)}\ \text{None of these}$

Solution 1

$\log_{5}\frac{(125)(625)}{25}$ can be simplified to $\log_{5}\ (125)(25)$ since $25^2 = 625$ . $125 = 5^3$ and $5^2 = 25$ so $\log_{5}\ 5^5$ would be the simplest form. In $\log_{5}\ 5^5$ , $5^x = 5^5$ . Therefore, $x = 5$ and the answer is $\boxed{\mathrm{(D)}\ 5}$

Solution 2

$\log_{5}\frac{(125)(625)}{25}$ can be also represented as $\log_{5}\frac{(5^3)(5^4)}{5^2}= \log_{5}\frac{(5^7)}{5^2}= \log_{5} 5^5$ which can be solved to get $5$

1950 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 24	Followed by Problem 26
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1950 AHSME Problems/Problem 25

Contents

Problem

Solution 1

Solution 2

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