You know the formula for comparing logarithms with two different bases.
What does this mean? Well, .
So the factor between using the log button and the ln button on your calculator is 2.3.
You say: that's not a problem anyhow, my calculator has both log and ln .
But what if you need to use a different base?

Calculate: . You should get 2.3. That is your factor. This means that logarithms base 10 are smaller than natural logs (absolute value).
Calculate: . You should get 0.69. That is your factor. This means that logarithms base 2 are bigger than natural logs (absolute value).