Question

solve the equation. check your answer.
ln(2x + 1)=4
x≈
(round to two decimal places as needed. use a comma to separate)

Explanation:

Step1: Use exponential - form conversion

If $\ln(2x + 1)=4$, then $e^{\ln(2x + 1)}=e^{4}$ according to the property $y = \ln x\Leftrightarrow x=e^{y}$. Since $e^{\ln a}=a$ for $a>0$, we have $2x + 1=e^{4}$.

Step2: Solve for x

First, isolate the term with x. Subtract 1 from both sides: $2x=e^{4}-1$. Then divide both sides by 2: $x=\frac{e^{4}-1}{2}$.

Step3: Calculate the value

We know that $e^{4}\approx54.59815$. So $x=\frac{54.59815 - 1}{2}=\frac{53.59815}{2}=26.799075\approx26.80$.

Answer:

$26.80$