Question

How do you solve `log_2(3x-5)>log_2(x+7)` and check the solutions?

Answer 1

`x>6`

Explanation:

`log_2 x` is a monotonically increasing function of `x`.

Hence, if `log_2(3x-5)>log_2(x+7)`

we have `3x-5>x+7`

or `3x-x>7+5`

or `2x>12`

or `x>6`
graph{lnx/ln2 [-0.17, 19.83, -4.04, 5.96]}