Question

If ${\log }_{10}2=a$ and ${\log }_{10}3=b$, then express $\log 12$ in terms of $a$ and $b$

• A. $2a+b$
• B. $2a-b$
• C. $3a+2b$
• D. $a+2b$

Answer 1

The correct option is A $2a+b$

Let $x=\log 12$
$⟹x=\log {3.2}^2$
$⟹x=\log 3+2\log 2$ (Using $\log a^b=b\log a,\log a.b=\log a+\log b$)
$⟹x=2a+b$.