Question

If ${25}^{x+1}=\frac{125}{5^x}:$ then the value of x is $\frac{1}{m}$
Value of $m$ is

• A. 2
• B. 4
• C. 3
• D. none of the above

Answer 1

The correct option is C 3

${25}^{x+1}=\frac{125}{5^x}$
$\therefore 5^{2x+2}=\frac{5^3}{5^x}$
By using law $\frac{a^m}{a^n}=a^{m-n}$, we get
$5^{2x+2}=5^{3-x}$
As base is same, we can equate the powers
$\therefore 2x+2=3-x$
$\therefore 3x=1$
$\therefore x=\frac{1}{3}$