How do you solve $3 e^{x} = 122$ $3e^x=122$ ?

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Answer 1 · 2016-06-09T11:21:21

Using the logarithm.

The way to "pull down" the $x$ $x$ from an exponential is to use the inverse function that is the logarithm.

$3 e^{x} = 122$ $3e^x=122$

$e^{x} = \frac{122}{3}$ $e^x=122/3$

Then we apply the logarithm on both sides

$ln (e^{x}) = ln (\frac{122}{3})$ $ln(e^x)=ln(122/3)$

Because the logarithm is the inverse of the exponential, they cancel each other on the left

$x = ln (\frac{122}{3}) \approx 3.7$ $x=ln(122/3)\approx3.7$ .

How do you solve 3ex=1223e^x=122?