Answer
$x\approx3.0444$
Work Step by Step
Given Expression
$3(2)^{x+2}+1=100$
Subtract 1 from both sides.
$3(2)^{x+2}=99$
Divide both sides.
$2^{x+2}=33$
Take log of both sides.
$\log2^{x+2}=\log33$
Power Rule of logarithms.
$(x+2)\log2=\log33$
Solve for $x$.
$x=(\frac{\log33}{\log2})-2$
$x\approx3.0444$