Question

if 125 power x=25/5 to the power x find the value of x

Answer 1

125powerx =25 /5 =

=5³ =5pwer X

if bases are equal powers must be equal so X=3

Answer 2

$125^x=\frac{25}{5^x} \\ \\ (5^3)^x=\frac{5^2}{5^x} \\ \\ (5^x)^3=\frac{5^2}{5^x}$

$5^2=(5^x)^3 \cdot 5^x \\ \\ 5^2=(5^x)^3 \cdot (5^x)^1 \\ \\ 5^2=(5^x)^{3+1} \\ \\ 5^2=(5^x)^4 \\ \\ 5^2=5^{4x}$

$2 = 4x \\ \\ 4x=2 \\ \\ x=\frac{2}{4} \\ \\ x=\bold{\frac{1}{2}}$