expand: In((3x-5)1/2 )/7

Answer 1

I believe you meant to type
In((3x-5)^1/2 )/7.

See the difference. You forgot to raise (3x - 5) to the 1/2 power.

Use the log rule for division:

ln(a/b) = ln(a) - ln(b).

ln((3x - 5)^1/2) - ln(7)

Note: (3x - 5)^1/2 is sqrt{3x - 5} in disguise.

Answer:

ln(sqrt{3x - 5}) - ln(7)

Answer 2

Perhaps one step further ...

ln((3x - 5)^1/2) - ln(7)
= (1/2) ln(3x-5) - ln 7