Question

If ${\log }_{10}2=a$ and ${\log }_{10}3=b$, then express $\log 2\frac{1}{4}$ in terms of $a$ and $b$

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

Answer 1

Answer: (C)

$2b-2a$

${\log }_{10}2=a{\log }_{10}3=b\log 2\frac{1}{4}=\log \left(\frac{3\times 3}{2\times 2}\right)=\log \left(\frac{3^2}{2^2}\right)=2\log 3-2\log 2=2b-2a$