Question

Let $N =10^{3 \log 2-2 \log \left(\log 10^3\right)+\log \left(\left(\log 10^6\right)^2\right)}$ where base of the logarithm is 10. The characteristic of the logarithm of $N$ to the base 3 , is equal to

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (B)

$ N=10^{ P } ; p =\log _{10} 8-\log _{10} 9+2 \log _{10} 6$
$p =\log \left(\frac{8 \cdot 36}{9}\right)=\log _{10} 32$
$\therefore N =10^{\log _{10} 32}=32$
Hence characteristic of $\log _3 32$ is 3 .