Question

when do you use the change-of-base formula for logarithms?

Answer 1

@Rainbow_Dash
If we had something like this
\[\frac{\log_{10} 8}{\log_{10} 2}=??\]
either we search in log tables for the value of numerator's and denominator's value
then we could find its value
But fortunately we have the formula
\[\frac{\log_a b}{\log_a c}=\log_c b\]
so
\[\frac{\log_{10} 8}{\log_{10} 2}=\log_2 8\]
it's simple , we don't need log tables for this

Answer 2

@Rainbow_Dash do you understand this?

Answer 3

I do, thank you