Question

Question #082ad

Answer 1

`x=9e^2+3`

Explanation:

Condense the logarithms using the rules:

• `log(A^B)=Blog(A)`
• `log(A)-log(B)=log(A/B)`

Then

`ln(x-3)-2ln(3)=2`

`ln(x-3)-ln(3^2)=2`

`ln((x-3)/3^2)=2`

Rewrite by exponentiating both sides with base `e` (that is, undo the logarithm):

`(x-3)/9=e^2`

From here, solving for `x` is simple:

`x=9e^2+3`