Question

What is x if Ln9+ln4x^2=2?

Answer 1

We wish to find `x` if `ln9 + ln(4x^2) = 2`. We will need to use some log rules here. Specifically, recall that:

`lnx + lny = ln(xy)`
`e^(ln(x)) = x`

Using the above two rules, we can quickly come to an answer.

`ln 9 + ln(4x^2) = 2` (Use Rule 1 to combine.)
`ln(9*4x^2) = 2`
`ln(36x^2) = 2` (Use Rule 2 and exponentiate both sides.)
`36x^2 = e^2`
`x^2 = e^2/(36) = (e/6)^2`
`x = pm e/6`