Easy way to compute logarithms without a calculator? I  would need to be able to compute logarithms without using a calculator, just on paper. The result should be a fraction so it is the most accurate. For example I have seen this in math class calculated by one of my class mates without the help of a calculator.   
$$\log_8128 = \frac 73$$
How do you do this?

Using $\log_xy=\dfrac{\log_ay}{\log_ax}$ and $\log(z^m)=m\log z$ where all the logarithms must remain defined unlike $\log_a1\ne\log_a(-1)^2$
$$\log_8{128}=\dfrac{\log_a(2^7)}{\log_a(2^3)}=\dfrac{7\log_a2}{3\log_a2}=?$$
Clearly, $\log_a2$ is non-zero finite for finite real $a>0,\ne1$
See Laws of Logarithms
