Question

Find the value of $x$, such that $5^{x+2}\times 5^6=5^{10}$.

• A. $1$
• B. $3$
• C. $2$
• D. $4$

Answer 1

The correct option is C $2$

Given, $5^{x+2}\times 5^6=5^{10}$
We know that $a^m\times a^n=a^{m+n}$
LHS $=5^{x+2}\times 5^6$
$=5^{x+2+6}$ $=5^{x+8}$
RHS $=5^{10}$
$\therefore 5^{x+8}=5^{10}$
$\therefore x+8=10$
$\therefore x=2$