Answer
$x=7.75$
Work Step by Step
RECALL:
$\log_b{x}= y \longrightarrow b^y=x$
Use the rule above to obtain:
$2^{5}=4x+1
\\32=4x+1$
Subtract $1$ on both sides of the equation to obtain:
$31=4x$
Divide $4$ on both sides of the equation to obtain:
$\dfrac{31}{4} = x
\\7.75=x$