# Solving an Exponential equation symbolically using Logarithms

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• August 31st 2010, 04:07 PM
Etiennedv
Solving an Exponential equation symbolically using Logarithms
I've been working on this problem and I just can't seem to figure it out.

Solve the expression https://webwork.colorado.edu/webwork...4cb9823ad1.png for https://webwork.colorado.edu/webwork...5b59f2bc11.png assuming that all other letters are positive constants.

I just keep running into dead ends where I have t on both sides or both t's on one side.
• August 31st 2010, 04:43 PM
wonderboy1953
What have you tried so far?
• August 31st 2010, 04:54 PM
pickslides
Is this ok?

$\displaystyle Pa^t = Vg^t$

$\displaystyle \frac{P}{V} = \frac{g^t}{a^t}$

$\displaystyle \frac{P}{V} = \left(\frac{g}{a}\right)^t$

$\displaystyle t = \log_{\frac{g}{a}}\frac{P}{V}$