Question

If pluto's average distance is approximately 100 times mercury's average distance, how many units on the logarithmic scale is pluto from mercury?

Answer 1

On a logarithmic scale, Pluto is 2 units from Mercury.

The default base for logarithms is 10, so saying that something is 2 units means that we are raising the base 10 to the power of 2.

$10^2=100$

Written as a logarithm, this would be:

$log_{10}100=2$

Whatever number you plug into the function, the answer will be whatever power the base needs to be raised to in order to equal the original number.

For example:

$log_{2}8=3$

because

$2^3 = 8$