Question

If e 5 x = 20 , then x

Answer 1

`x=\frac{\ln(20)}5`

`x \approx 0.599`

Explanation:

We can solve for
`x` in the expression:

`e^(5x)=20`

by taking the natural log of both sides:

`\ln(e^(5x)) = \ln(20)`

↓ simplifying the left side

`5x = \ln(20)`

↓ dividing both sides by 5

`\boxed{x=\frac{\ln(20)}5 \approx 0.599}`

Further Note

The natural log function returns the exponent that the mathematical constant
`e` must be raised to so that the resulting value is the number being operating on.

For example:

`\ln(e^2) = 2`

because
`e` to the power of
`2` results in
`e^2`.