Answer
$x=\dfrac{\log45}{\log3}-1\approx2.464974$
Work Step by Step
$2(5+3^{x+1})=100$
First, let's solve for $3^{x+1}$:
$5+3^{x+1}=\dfrac{100}{2}$
$5+3^{x+1}=50$
$3^{x+1}=50-5$
$3^{x+1}=45$
Apply $\log$ to both sides of the equation:
$\log3^{x+1}=\log45$
The exponent $x+1$ can be taken down to multiply in front of its respective $\log$:
$(x+1)\log3=\log45$
Solve for $x$:
$x+1=\dfrac{\log45}{\log3}$
$x=\dfrac{\log45}{\log3}-1\approx2.464974$
