Problem: What is the value of [10(510100)]2?\left[\log _{10}\left(5 \log _{10} 100\right)\right]^{2}?[log10(5log10100)]2?
Answer Choices:
A. 1050\log _{10} 50log1050
B. 252525
C. 101010
D. 222
E. 111 Solution:
[10(510100)]2=[10(5⋅2)]2=12=1\left[\log _{10}\left(5 \log _{10} 100\right)\right]^{2}=\left[\log _{10}(5 \cdot 2)\right]^{2}=1^{2}=1[log10(5log10100)]2=[log10(5⋅2)]2=12=1