Answer
$x=\frac{e^{3.4}-5}{2}\approx12.4821$
Work Step by Step
We are given the equation $\ln(2x+5)=3.4$. To solve for x, remember that the base of a natural logarithm is understood to be $e$.
Therefore, $\ln(2x+5)=log_{e}(2x+5)=3.4$.
If $b\gt0$ and $b\ne1$, then $y=log_{b}x$ means $x=b^{y}$ for every $x\gt0$ and every real number $y$.
Therefore, $2x+5=e^{3.4}$.
Subtract 5 from both sides.
$2x=e^{3.4}-5$
Divide both sides by 2.
$x=\frac{e^{3.4}-5}{2}\approx12.4821$
