1. ## Log

Hi guys. I'm stuck on this one.

2*e^(-x) = 3*e^(0,1x)

Any help would be appreciated.

2. Originally Posted by Alvy
Hi guys. I'm stuck on this one.

2*e^(-x) = 3*e^(0,1x)

Any help would be appreciated.
Hi Alvy,

Do this:

$\ln 2e^{-x}=\ln 3e^{.1x}$

$\ln 2 + (-x)=\ln 3 + .1x$

$-1.1x=\ln 3 - \ln 2$

$x=\frac{\ln 3 - \ln 2}{-1.1}$

3. Hello, Alvy!

Another approach . . .

Solve for $x\!:\;\;2e^{-x} \:=\: 3e^{0.1x}$

We have: . $3e^{0.1x} \;=\;2e^{-x}$

Multiply by $\frac{e^x}{3}\!:\;\;e^{1.1x} \;=\;\frac{2}{3}$

$\text{Take logs: }\;\ln\left(e^{1.1x}\right) \;=\;\ln\left(\frac{2}{3}\right) \quad\Rightarrow\quad 1.1x\underbrace{\ln(e)}_{\text{This is 1}} \;=\;\ln\left(\frac{2}{3}\right)$

Therefore: . $1.1x \;=\;\ln\left(\frac{2}{3}\right) \quad\Rightarrow\quad x \;=\;\frac{1}{1.1}\ln\left(\frac{2}{3}\right)$