Question

if 125^x=25/5^x, then find x​

Answer 1

» Question -

$125^x = \frac{25}{5^x}, then\:find\:x$

» Solution -

We know that,

${\pink{\boxed{(a^m)^n = a^{mn}}}}\\ \\ \\ {\purple{\boxed{\frac{a^m}{a^n} = a^{m-n}}}}$

125 = 5³

25 = 5²

$125^x = \frac{25}{5^x}\\ \\ \\ = (5^3)^x = \frac{5^2}{5^x}\\ \\ \\ = 5^{3x} = 5^{2-x}\\ \\ \\ when\:the\:base\:is\:equal\:powers\: also\: become\:equal\\ \\ \\ 3x = 2-x \\ \\ \\ 4x = 2\\ \\ \\ x = \frac{2}{4}\\ \\ \\ {\pink{\boxed{x = \frac{1}{2}}}}$

laws of exponents-

$a^m \times a^n = a^{m+n}\\ \\ \\ a^0 = 1\\ \\ \\(a^m)^n = a^{mn}\\ \\ \\ \frac{a^m}{a^n} = a^{m-n}\\ \\ \\ a^{-m} = \frac{1}{a^m}$