Question

Please Solve this Question

Answer 1

$\large\underline{\text{Solution}}$

Let $5^{x}=t$.

Then we get a cubic equation.

$\implies\dfrac{t^{3}}{5t}=125t$

$\implies t^{3}=625t^{2}$

$\implies t^{2}(t-625)=0$

$\implies t=0\text{ or }t=0\text{ or }t=625$

By substitution

$\implies5^{x}=0\text{ or }5^{x}=0\text{ or }5^{x}=5^{4}$

As $5^{x}>0$ for real $x$, we reject the first two solutions.

Then we are left with $5^{x}=5^{4}$. So the solution is $x=4$.