How do you solve e^(12-5x) -7 = 123?

Jul 30, 2015

$x = \frac{1}{5} \left(12 - \ln \left(130\right)\right)$

Explanation:

 e^(12−5x)−7 = 123
 => e^(12−5x) = 123 + 7 = 130  (Add 7 to both sides)
 => 12−5x = ln(130)  (Take natural logarithm on both sides)
 => −5x = -12 + ln(130)  (Add -12 to both sides)
$\implies 5 x = 12 - \ln \left(130\right)$ (Multiply by -1)
$\implies x = \frac{1}{5} \left(12 - \ln \left(130\right)\right)$ (Divide by 5 on both sides)

If you need, you may use a calculator to get $\log \left(130\right) = 4.8675$. Put this value to get $x = 1.4265$.