Question

please solve 125^(x-1) = 5^(3x-2) -500

Answer 1

Correct Question

Solve $125^{x-1}=5^{3x-2}+500$

To Find

Value of x

Solution

$\implies\sf\:125^{x-1}=5^{3x-2}+500$

$\implies\sf\:125^{x-1}-5^{3x-2}=500$

$\implies\sf\:5^3(^{x-1})-5^{3x-2}=500$

$\implies\sf\:5^{3x-3}-5^{3x-2}=500$

$\implies\sf\:5^{3x}(5^{-3}-5^{-2}=500$

$\implies\sf\:5^{3x}(\frac{1}{125}-\frac{1}{25})=500$

$\implies\sf\:5^{3x}(\frac{5-1}{25})=500$

$\implies\sf\:5^{3x}(\frac{4}{25})=500$

$\implies\sf\:5^{3x}=\frac{25}{4}500$

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

$\implies\sf\:5^{3x}=5^5$ (same base)

$\implies\sf\:{3x}=5$

$\therefore\sf\:x=\frac{5}{3}$

Hence the value of $\therefore\sf\:x=\frac{5}{3}$