Question

How do you solve `log_3 4x^2-log_3 8=2`?

Answer 1

`x = 3 sqrt(2)` and `x = -3 sqrt(2)`

Explanation:

`log_3(4x^2)-log_3 8 = log_3(4x^2/8) = log_3 3^2`
so follows
`x^2/2=3^2` having two solutions
`(x/sqrt(2))^2-3^2=(x/sqrt(2)+3)(x/sqrt(2)-3) = 0`
The solutios are
`x = 3 sqrt(2)` and `x = -3 sqrt(2)`