solve for x
5^x = 4 ^ (x+1)
You could use logarithms directly but I fancy using the laws of indices and of logarithms for a change
$\displaystyle 5^x = 4 \cdot 4^x$
$\displaystyle x\,\ln(5) = \ln(4) + x\,ln(4)$
Simplify to find x. If your answer book uses $\displaystyle \ln(2)$ then recall that $\displaystyle 4=2^2$