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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- Sep 8th 2008, 01:05 PMdm10solve 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. - Sep 8th 2008, 01:24 PMmr fantastic
- Sep 8th 2008, 01:41 PMdm10
thanks for the help.

I have one more if you don't mind.

100000=500*2^t/(1/2) - Sep 8th 2008, 03:11 PMmr fantastic
- Sep 8th 2008, 03:24 PMdm10
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.

- Sep 8th 2008, 03:34 PMmr fantastic
$\displaystyle \Rightarrow 200 = 2^{t/(1/2)} = 2^{2t}$ since $\displaystyle \frac{t}{1/2} = 2t$.

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

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

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.