Homework Help: algebra 2 logs and trig

Posted by Teddy on Friday, August 13, 2010 at 11:07am.

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.

algebra 2 logs and trig - bobpursley, Friday, August 13, 2010 at 11:46am
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.
algebra 2 logs and trig - Teddy, Friday, August 13, 2010 at 11:57am
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)
algebra 2 logs and trig - bobpursley, Friday, August 13, 2010 at 9:29pm
no, of course not.
did you mean this?
2log2 cscx= log4 cscx
That is correct.

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