Question

If $5^{3x}=125\text{and}{10}^y=0.001$, find x and y.

Answer 1

It is given that $5^{3x}=125\text{and}{10}^y=0.001$.
Now,
$$\begin{gathered} 5^{3x}=125 \\ \Rightarrow 5^{3x}=5^3 \\ \Rightarrow 3x=3 \\ \Rightarrow x=1 \end{gathered}$$
And,
$$\begin{gathered} {10}^y=0.001 \\ \Rightarrow {10}^y=\frac{1}{1000} \\ \Rightarrow {10}^y={10}^{-3} \\ \Rightarrow y=-3 \end{gathered}$$
Hence, the values of x and y are 1 and −3, respectively.