Which value of m gives a non-integer?

Name: Which value of m gives a non-integer?
Uploaded: 2011-02-08
Description: Solution Take the logarithm for both sides and solve for $n$: \begin{align}m^n&=256\\ \log{m}^n&=\log{256}\\n\log m&=\log{256}\\n&=\frac{\log256}{\log m} \end{align}The value of $m$ that will give a non-integer is 8:$$n=\frac{\log256}{\log 8}\approx 2.7$$ which is non intiger.Answer: B

8. If $m^{n}=256$, $m$ and $n$ are integers, which of the following could NOT be a value of $m$?

Take the logarithm for both sides and solve for $n$: \begin{align}m^n&=256\\ \log{m}^n&=\log{256}\\n\log m&=\log{256}\\n&=\frac{\log256}{\log m} \end{align}

The value of $m$ that will give a non-integer is 8:$$n=\frac{\log256}{\log 8}\approx 2.7$$ which is non intiger.

Answer: B