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