Base change

In some situations we may find calculations involving several logarithms on different bases. Since logarithmic properties are only valid for logarithms on the same basis, it is necessary to convert the logarithms of different bases to a single convenient base first.

This conversion is called base change. To make a base change The to another base B used:

For example, note this question applied to an entrance exam:

Knowing that log a = L and log b = M, so the logarithm of a in base b is:
a) L + M
b) L-M
c) L.M
d) M / L
e) L / M

The problem provided the logarithm of The in base 10 and asked for the logarithm of The in the base B. Applying the base change formula, we will transform for base 10:

From the statement, we know that log a = L and log b = M, so the answer is:

Next: Online Calculation of Logarithms