find the domain of..

yeh kaisa atyachar .. so many bases !!

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,∞)

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 !

is dis condition sufficient??
i think we need to impose two more conditions!
1. log₃ log₂ (2x³ + 5x² - 14x) >0
2. log₂ (2x³ + 5x² - 14x) > 0