Start with the substitution \(u = 4^x\). The equation becomes:

\(u + 16 = 16u\)

Rearrange to solve for \(u\):

\(16u - u = 16\)

\(15u = 16\)

\(u = \frac{16}{15}\)

Since \(u = 4^x\), we have:

\(4^x = \frac{16}{15}\)

Take the logarithm of both sides:

\(x \log(4) = \log\left(\frac{16}{15}\right)\)

\(x = \frac{\log\left(\frac{16}{15}\right)}{\log(4)}\)

Calculate \(x\) to 3 significant figures:

\(x \approx 0.0466\)