[Algebra]
Problem: If $3\left(8^{x}\right)+5\left(8^{x}\right)=2^{61}$, what is the value of the real number $x$ ?

Solution: We obtain successively

$$
\begin{aligned}
3\left(8^{x}\right)+5\left(8^{x}\right) & =2^{61} \\
8\left(8^{x}\right) & =2^{61} \\
8^{x+1} & =2^{61} \\
\left(2^{3}\right)^{x+1} & =2^{61} \\
2^{3(x+1)} & =2^{61}
\end{aligned}
$$

Thus, $3(x+1)=61$ and so $3 x+3=61$ which gives $3 x=58$ or $x=\frac{58}{3}$.

Final answer: $\frac{58}{3}$