Natural Logs.

[WTF?]

I have quick question.

e^(x-1) = 25


I try to set it up as:

x-1 ln = ln25

Where to from there? :?

 

[Gene]

Its
x-1 = ln(25)

 

[soroban]

Hello, WTF?

You're almost there . . .

\(\displaystyle e^{x-1}\; =\; 25\)

I try to set it up as: \(\displaystyle \,(x-1)\ln(e)\:=\:\ln(25)\)
Where to from there? \(\displaystyle \;\) . . . solve for x

It may be clearer if you include all the steps . . .

We have: \(\displaystyle \,e^{^{x-1}}\:=\:25\)

Take logs: \(\displaystyle \,\ln(e^{^{x-1}})\:=\;\ln(25)\)

Then: \(\displaystyle \,(x-1)\cdot\ln(e)\:=\:\ln(25)\)

Since \(\displaystyle \ln(e)\,=\,1\), we have: \(\displaystyle \,x\,-\,1\:=\:\ln(25)\;\;\Rightarrow\;\;x\:=\:\ln(25)\,+\,1\)