Which value of m gives a non-integer?

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

  1. 2
  2. 8
  3. 4
  4. 16
  5. 256

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