Start by converting them to the same base...
Would be to much trouble to ask you to show me?
is it okay to leave it as a inequality?
Since the base is the same, you can actually make this log (2x/(3(4x-5))) >1 or
log (2x/(12x-15)) >1. And this simply means that (2x/12x-15)>10.
Temporarily assuming that 12x-15 is positive (x>1.25), you can multiply each side by this and get
2x>120x -150. Then 2x +150>120x, then 150>118 x. Then x<150/118 (but still greater than 1.25).
Temporarily assuming that 12x-15 is negative (x<1.25), you can do the same stuff with the sign pointing the other way, 150<118x , then x>150/118, but this is a contradiction.
So I'm sticking with 1.25<x<150/118 (this fraction is approx 1.271 btw, so a narrow value range)
Yes, is the correct solution for
I sure that Prove It assumed that what you meant by log_2x was , etc. The underscore symbol, "_" , generally means that what follows is a subscript.
I tried to solve it assuming that the bases were 2 & 3 as Prove It reasonably assumed. This does give the approximate answer: x>67.7721.
Assume:
Changing the bases gives:
Multiply both sides by ln(2) and ln(3).
Use each side as the exponent with base e.
Solve it graphically.