Question

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

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

Answer 1

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

$\log x=m+n$
$\log y=m-n$
Now, $\log \frac{10x}{y^2}=\log 10x-\log y^2$
= $\log 10+\log x-2\log y$
= $1+m+n-2(m-n)$
= $1+m+n-2m+2n$
= $1-m+3n$