algebra 2 logs and trig
posted by Teddy on .
log(base 2)cotx  2log(base 4)csc2x = log(base 2)cosx
the answer should be x = pi/3, 5pi/3
not sure how to work it out though, any help? I tried canceling the bases but that led to a dead end.

Think about log2 and log4. If N is a number, log2(N)=1/2 log4(N)
I am uncertain if the second term is csc^2 x or csc 2x. But my hint above should lead you to the solution. 
It's csc 2x, and I got it down to this before but I don't know if I can use your hint from there or if I should start from square one:
log(base 2)csc(x) = log(base 4)csc(4x^2)
Would that become the following?
log(base 2)csc(x) = 2log(base2)csc(4x^2) 
no, of course not.
did you mean this?
2log2 cscx= log4 cscx
That is correct.