Question

How do you evaluate `5e^(3x+7)=21`?

Answer 1

`x=(ln(21/5)-7)/3approx-1.8550`

Explanation:

Divide both sides by `5`.

`e^(3x+7)=21/5`

To undo the exponential function with a base of `e`, take the logarithm of both sides with base `e`. Note that `log_e(x)` is the natural logarithm, denoted `ln(x)`.

`ln(e^(3x+7))=ln(21/5)`

`3x+7=ln(21/5)`

Subtract `7` from both sides.

`3x=ln(21/5)-7`

Divide both sides by `3`.

`x=(ln(21/5)-7)/3approx-1.8550`