Question

16^(x+4)=8^(3x-2)
Solve

Answer 1

Convert it into base 2 first:
\[\large 2^{4(x+4)}=2^{3(3x-2)}\\
\large 2^{4x+16}=2^{9x-6}\]
Log both sides:
\[\large \log \left(2^{4x+16}\right)=\log\left(2^{9x-6}\right)\\
\large (4x+16) \log 2 = (9x-6) \log 2\\
\large (4x)\log 2 + 16 \log 2 = (9x)\log 2 - 6 \log 2\\
\large (4x) \log 2 - (9x) \log 2 = -16 \log 2 - 6 \log 2 \\
\large x\left(4 \log 2 - 9 \log 2 \right) = - 22 \log 2 \\
\large x \left( -5 \log 2 \right) = - 22 \log 2 \\
\large x = \frac{-22 \log 2 }{- 5 \log 2}\\
\large x = \frac{22}{5}\]