Question

plz answer this question​

Answer 1

Question :-

If $\sf 5^{3x-1} \div 25 = 125$, find the value of x.

Answer :-

$\implies\sf 5^{3x-1} \div 25 = 125$

$\implies\sf \dfrac{5^{3x-1}}{25} = 125$

$\implies\sf \dfrac{5^{3x-1}}{5^2} = 125$

$\implies\sf 5^{3x-1-2} = 125$

$\implies\sf 5^{3x-3} = 125$

$\implies\sf 5^{3x-3} = 5^3$

Base are equal, so power will also ne equal :-

$\implies\sf 3x - 3 = 3$

$\implies\sf 3x = 3 + 3$

$\implies\sf x = \dfrac{6}{3}$

$\implies\sf x = 2$

Value of x = 2

Verification :-

$\sf LHS = 5^{3x-1} \div 25$

$\implies\sf LHS = \dfrac{5^{3(2)-1}}{25}$

$\implies\sf LHS = \dfrac{5^{6-1}}{5^2}$

$\implies\sf LHS = \dfrac{5^5}{5^2}$

$\implies\sf LHS = 5^{5-2}$

$\implies\sf LHS = 5^3$

$\implies\sf LHS = 125$

$\sf RHS = 125$

LHS = RHS

Hence, verified.

Extra information :-

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