Question

How do you solve `4000= 200e ^ { 8x }`?

Answer 1

Take the natural log of both sides to bring the `x` exponent down and then solve for `x`.

Explanation:

We can take a log of both sides firstly, doing this we get: `ln(4000) = ln(200e^(8x))`

We can now separate the logs like so:
`ln(4000) = ln(200) + ln(e^(8x))`

Moving the exponent in front of the log:
`ln(4000) - ln(200) = 8xln(e)`

Simplifying:
`ln(4000/200) = 8xcancel(ln(e)) = 8x`

`ln(20) = 8x -> ln(20)/8 = x`