find the domain of..

log₅log₃log₂(2x³+5x²-14x) > 0
==> log₃log₂(2x³+5x²-14x) > 1
==> log₂(2x³+5x²-14x) > 3
==> (2x³+5x²-14x) > 2³
==> 2x³+5x²-14x - 8 > 0
==> x=2 is a solution by inspection

So, 2x³+5x²-14x - 8 = (x-2)(2x²+9x+4)
= (x-2)(2x+1)(x+4)

So, x = (-4,-1/2) U (2,∞)

log ₅ log₃ log₂ (2x³+5x²-14x) > 0

=> log₃ log₂ (2x³+5x²-14x) > 1

=> log₂ (2x³+5x²-14x) > 3

=> 2x³+5x²-14x > 8

=> 2x³+5x²-14x-8 > 0

i hope u can solve this now. :)

ya. shall i solve it too.!!? or let her try this !?

well the final answer is (-4,-1/2) u (2,∞)

correct me if i am wrong !

ohk.. i will try after dis!!![1]

@surbhi in the steps of solution:
log₃log₂(2x³+5x²-14x) > 1 so obviously it is >0
and log₂(2x³+5x²-14x) > 3 so obviously it is > 0 as well