Question

Let $x$ is the value of satisfying the equation $5^{{\log }_{10}x}=50-x^{{\log }_{10}5}$. Then find the value of $\frac{x}{50}$.

Answer 1

Answer: 2

Put $5^{{\log }_{10}x}=t$
$2t=50\Rightarrow t=25$
$\Rightarrow 5^{{\log }_{10}x}=5^2\Rightarrow x=100\Rightarrow \frac{x}{50}=2$