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Math Help - Logarithm questions

  1. #1
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    Logarithm questions

    How would you solve these equations?


    Sorry about the small thumbnails! As for the first question, I can only simplify the log(16,x) into log(4,sqrt(x)), but doing so seems to further complicate matters. How do I set aside x by itself? Same dilemma for the trig logarithm!!!
    Attached Thumbnails Attached Thumbnails Logarithm questions-img-1-.gif   Logarithm questions-wolframalpha-2_tan_x__pi_4___2_0_25____sin_2_x_pi_4__cos2x__1__input__2013_08_22_0047.gif  
    Last edited by facebook; August 21st 2013 at 09:50 PM.
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  2. #2
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    Re: Logarithm questions

    Hey facebook.

    Is the second one meant to be equal to something?

    Hint: Remember that log_a(b) = log_x(b)/log_x(a) where log_x is the logarithm in base x which is defined as log_x(y) = ln(y)/ln(x) where ln is the natural logarithm. Also remember that a^log_a(x) = x.
    Last edited by chiro; August 21st 2013 at 10:55 PM.
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  3. #3
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    Re: Logarithm questions

    Quote Originally Posted by chiro View Post
    Hey facebook.

    Is the second one meant to be equal to something?
    Yes! My mistake! It is supposed to equal 0. Essentially the problem is to find the zeros of the function!
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