Question

What is the soluton to the equation e^3x=12

Answer 1

`x=(ln(12))/(3)`

Explanation:

We can solve this equation by taking the natural log of both sides.

This gives us the equation:
`ln(e^(3x))=ln(12)`

And the definition of natural log is basically, "what do I have to raise e to, to get this result"

The result is just e^3x, so I have to raise e to what? Well that's just 3x, you could also use log properties to bring the exponent in front and realize ln(e) = 1

So this gives us:
`3x=ln(12)`

Now divide both sides by 3:
`x=(ln(12))/(3)`