Question

solve (9) to the power 5x = (9 power 4 ) to the power x ÷ 9 power 2

step by step

answer me properly and I will mark as brainliest ​

Answer 1

Question :-

$\sf {(9)}^{5x} = \frac{( {9}^{4}) ^{x} }{ {9}^{2} }$

Answer :-

→ $\sf 9^{5x} = \frac{9^{4 \times x}}{9^2}$

→ $\sf 9^{5x} = \frac{9^{4x}}{9^2}$

→ $\sf 9^{5x} = 9^{4x - 2}$

As base are same, power will also be same -

→ $\sf 5x = 4x - 2$

→ $\sf 5x - 4x = -2$

→ $\sf x = -2$

Value of x = -2

Additional information :-

$\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end{gathered}$