Math Help - Exponential Equation help!

1. Exponential Equation help!

How would I go about doing problems such as

e^x+1=1/e

and

e^x+4=1/e^2x

Thanks!

2. Originally Posted by The Masked Trumpet

e^x+1=1/e
$e^x+1=\frac{1}{e}$

$e^x=\frac{1}{e}-1$

$x=\ln\left(\frac{1}{e}-1\right)$

Originally Posted by The Masked Trumpet
How
e^x+4=1/e^2x
$e^x+4=\frac{1}{e^{2x}}$

$e^{2x}(e^x+4)=1$

$e^{2x}(e^x+4)=1$

$e^{3x}+4e^{2x}=1$

Now substituting

$a = e^x$

$a^{3}+4a^{2}-1=0$

You now have to solve this cubic.

3. K, I think I understand those.

How would I do one like this,

e^(x+1)=1/e

4. You should consider this

$e^x = y \Rightarrow x = \log_e(y)$

or

$e^x = y \Rightarrow x = \ln(y)$

Therefore using the second transformation

$e^{x+1}=\frac{1}{e}$

$x+1=\ln\left(\frac{1}{e}\right)$

$x=\ln\left(\frac{1}{e}\right)-1$