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Math Help - Logarithmic Functions

  1. #1
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    Logarithmic Functions

    1) ln(2t+1)=2-lnt Solve for t.
    I just want to know whether I need to move lnt to the left side in order to solve the equation or can I just leave the equation as is and multiply both sides by e.

    2) This problem has been bothering me for a while.
    Differentiate y=10^tan(theta)

    I tried to solving it earlier but I got stuck:
    log10y=tan(theta)
    So now can I use implicit differentiation?

    Thank you!
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  2. #2
    Super Member bigwave's Avatar
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    now or later

    you will have all the terms with t to one side eventually...
    might as well do it early on....doesn't have to be first step tho..
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  3. #3
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    Quote Originally Posted by yzobel View Post
    1) ln(2t+1)=2-lnt Solve for t.
    I just want to know whether I need to move lnt to the left side in order to solve the equation or can I just leave the equation as is and multiply both sides by e.

    You don't multiply by e: you APPLY e at both sides. But first move ln t to the left side:

    \ln((2t+1)t)=2\Longrightarrow 2t^2+t=e^2...

    2) This problem has been bothering me for a while.
    Differentiate y=10^tan(theta)

    I tried to solving it earlier but I got stuck:
    log10y=tan(theta)
    So now can I use implicit differentiation?

    Indeed: \frac{1}{y}dy=\frac{1}{\cos^2\theta}d\theta and etc.

    Tonio

    Thank you!
    .
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