Question

If $\log x=m+n$ and $\log y=m-n$, then value of $\log \frac{10x}{y^2}$ in terms of $m$ and $n$ is

• A. $1-m-3n$
• B. $1+m+3n$
• C. $1+m-3n$
• D. $1-m+3n$

Answer 1

The correct option is D $1-m+3n$

Let $k=\log \frac{10x}{y^2}$
$⟹k=\log 10+\log x-2\log y$ (Using $\log a.b=\log a+\log b,\log \frac{a}{b}=\log a-\log b$)
$⟹k=1+m+n-2m+2n$
$⟹k=1-m+3n$