Answer
$x\approx25.6765$
Work Step by Step
Given Expression
$2(1.05)^x+3=10$
Subtract 3 from both sides.
$2(1.05)^x=7$
Divide both sides by 2.
$(1.05)^x=\frac{7}{2}$
Take log of both sides.
$\log(1.05)^x=\log\frac{7}{2}$
Power Rule of logarithms.
$x\log1.05=\log\frac{7}{2}$
Solve for $x$.
$x=\frac{\log\frac{7}{2}}{\log1.05}$
$x\approx25.6765$