# Math Help - [SOLVED] natural logarithms

1. ## [SOLVED] natural logarithms

i am very confused and i need help solving this equation. thanks.

4 ln 2x=ln e^2

2. Hello,barb!

$4\!\cdot\!\ln(2x) \:= \:\ln\left(e^2\right)$
First of all: . $\ln(e^2) \;=\;2$

So we have: . $4\!\cdot\!\ln(2x) \;=\;2$

Divide by 4: . $\ln(2x) \;=\;\frac{1}{2}$

Exponentiate: . $2x \;=\;e^{\frac{1}{2}}$

Divide by 2: . $\boxed{x \;=\;\frac{1}{2}e^{\frac{1}{2}}}$