1964 AHSME Problems/Problem 1

Problem

What is the value of $[\log_{10}(5\log_{10}100)]^2$ ?

$\textbf{(A)}\ \log_{10}50 \qquad \textbf{(B)}\ 25\qquad \textbf{(C)}\ 10 \qquad \textbf{(D)}\ 2\qquad \textbf{(E)}\ 1$

$[\log_{10}(5\log_{10}100)]^2$

Since $10^2 = 100$ , we have $\log_{10} 100 = 2$ , so:

$[\log_{10}(5\cdot 2)]^2$

Multiply:

$[\log_{10}(10)]^2$

Since $10^1 = 10$ , we have $\log_{10} 10 = 1$ , so:

$[1]^2$

$1$

$\fbox{E}$ .

1964 AHSC (Problems • Answer Key • Resources)
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