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algebra 2 logs and trig

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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 -

    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 -

    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 -

    no, of course not.
    did you mean this?
    2log2 cscx= log4 cscx
    That is correct.

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