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1. What is the value of ${[lo g_{10} (5lo g_{10} 100)]}^{2}$ = ?

A. 1

B. 2

C. 10

D. 25

Solution:

\begin{aligned} {[lo g_{10} (5lo g_{10} 100)]}^{2} \\ = {[lo g_{10} {5lo g_{10} {(10)}^{2}}]}^{2} \\ = {[lo g_{10} (5 \times 2)]}^{2} \\ = {(lo g_{10} 10)}^{2} \\ = 1 \end{aligned}

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