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 Question from Samantha, a student: I can't seem to understand how to solve for x when it is in power form, here is the equation: 4=(1+.08)^x

Hi Samantha,

Logarithms will help. The property of logarithms that is helpful here is that

$\log(a^b) = b \log(a).$

Thus if you have, for example

$6 = 1.34^x$

you can take the logarithm of both sides and the equation becomes

$\log(6) = \log\left((1.34^x\right) = x \log(1.34)$

and hence

$x = \frac{\log(6)}{\log{(1.34)}} = \frac{0.7782}{0.1271} = 6.12.$

Now try this with $4 = 1.08^x$.

Penny

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