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Math Help - solve for t

  1. #1
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    solve for t

    50000=100*2^(t/3)

    Solve for t.

    I'm not sure how to solve for t when it's an exponent and a fraction.
    Please help because I need the answer to this very soon.
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  2. #2
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    Quote Originally Posted by dm10 View Post
    50000=100*2^(t/3)

    Solve for t.

    I'm not sure how to solve for t when it's an exponent and a fraction.
    Please help because I need the answer to this very soon.
    \Rightarrow 500 = 2^{t/3} \Rightarrow \log_{10} 500 = \log_{10} 2^{t/3} = \frac{t}{3} \log_{10} 2 \Rightarrow \frac{t}{3} = \frac{\log_{10} 500}{\log_{10} 2} \Rightarrow t = \, ....
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  3. #3
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    thanks for the help.

    I have one more if you don't mind.

    100000=500*2^t/(1/2)
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  4. #4
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    Quote Originally Posted by dm10 View Post
    thanks for the help.

    I have one more if you don't mind.

    100000=500*2^t/(1/2)
    Do you mean 100000 = (500) \times 2^{t/(1/2)}?
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  5. #5
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    Yes that's right. It's alright though. I solved it by myself but I'd appreciate if you posted your answer so I can check my work.
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  6. #6
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    Quote Originally Posted by mr fantastic View Post
    Do you mean 100000 = (500) \times 2^{t/(1/2)}?
    Quote Originally Posted by dm10 View Post
    Yes that's right. It's alright though. I solved it by myself but I'd appreciate if you posted your answer so I can check my work.
    \Rightarrow 200 = 2^{t/(1/2)} = 2^{2t} since \frac{t}{1/2} = 2t.

    Then \log_{10} 200 = \log_{10} 2^{2t} = 2t \log_{10} 2 \Rightarrow 2t = \frac{\log_{10} 200 }{\log_{10} 2} \Rightarrow t = \frac{\log_{10} 200 }{2 \log_{10} 2}.

    This answer can also be written as t = \frac{\log_{10} 200 }{\log_{10} 4}.

    The reason I use base 10 rather than base 2 is so that a scientific calculator can be used to get a decimal approximation of the answer if required.
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