evaluating logarithm without a calculator

[charlesjoy]

Is there a way to solve this problem without a calculator? the problem asks me to use a calculator to evaluate the logarithm

log 0.0576

 

[BigGlenntheHeavy]

You could use a book of logs, in which you'll probably have to interpolate (nasty grunt work), but why if you have a calculator?

 

[daon]

If its a friendly base, you can estimate using a graph.

For instance, log base 2, plot the points:

..., (1/32=0.03125, -5), (1/16=0.0625, -4), (1/8=0.125,-3), (1/4=.25, -2), (1/2=0.5, -1), (1,0), (2,1), (4,2), ...

Connect them with a smooth curve and use you scale to estimate the value.

For log_2(0.0576) you can see its "close" to -4, but a little less. Using a good scale you could come up with -4.1.

 

[daon]

Here's another way to simplify an approximation when using a graph.

log(0.0576) = log(576*10^(-4)) = log(576)-4
~ log(6*10^2) - 4
~ log(6) - 2