# solve for t

• September 8th 2008, 01:05 PM
dm10
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.
• September 8th 2008, 01:24 PM
mr fantastic
Quote:

Originally Posted by dm10
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.

$\Rightarrow 500 = 2^{t/3} \Rightarrow \log_{10} 500 = \log_{10} 2^{t/3} = \frac{t}{3} \log_{10} 2 \Rightarrow \frac{t}{3} = \frac{\log_{10} 500}{\log_{10} 2} \Rightarrow t = \, ....$
• September 8th 2008, 01:41 PM
dm10
thanks for the help.

I have one more if you don't mind.

100000=500*2^t/(1/2)
• September 8th 2008, 03:11 PM
mr fantastic
Quote:

Originally Posted by dm10
thanks for the help.

I have one more if you don't mind.

100000=500*2^t/(1/2)

Do you mean $100000 = (500) \times 2^{t/(1/2)}$?
• September 8th 2008, 03:24 PM
dm10
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.
• September 8th 2008, 03:34 PM
mr fantastic
Quote:

Originally Posted by mr fantastic
Do you mean $100000 = (500) \times 2^{t/(1/2)}$?

Quote:

Originally Posted by dm10
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.