Math CentralQuandaries & Queries


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:


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 $4 = 1.08^x$.


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