Solve $3\log_{10}(x-15) = \left(\frac{1}{4}\right)^x$ $$3\log_{10}(x-15) = \left(\frac{1}{4}\right)^x$$
I am completely lost on how to proceed. Could someone explain how to find any real solution to the above equation?

Put 
\begin{equation*}
f(x)  = 3\log_{10}(x - 15) - \left(\dfrac{1}{4}\right)^x.
\end{equation*}
We have $f$ is a increasing function on $(15, +\infty)$.
Another way,
$f(16)>0 $ and $f(17)>0$. Therefore the given equation has only solution belongs to $(16,17)$.
