Question

If ${\log }_{10}2=a$ and ${\log }_{10}3=b$, then express $\log 3\frac{1}{8}$ in terms of $a$ and $b$

• A. $2+5a$
• B. $2-5a$
• C. $2-a$
• D. $2+a$

Answer 1

Answer: (B)

$2-5a$

${\log }_{10}2=a{\log }_{10}3=b\log 3\frac{1}{8}=\log \frac{25}{8}=\log \frac{25\times 4}{8\times 4}=\frac{\log 100}{\log 32}=2{\log }_{10}10-\log 2^5=2-5\log 2=2-5a$