Final answer:
The change of base formula allows you to calculate the logarithm of a number in any base by expressing it in terms of a logarithm with a base that is conveniently calculable, especially when calculator support for the original base is not available.
Step-by-step explanation:
The change of base formula is used to rewrite logarithms in terms of logarithms of another base. This is particularly useful when you need to compute logarithms by hand or with a calculator that does not support direct calculation in the given base. The formula can be derived using the property of logarithms that states loga(b) = log(c)/(logc(a)) where c is the new base.
To rewrite loga(x) in terms of base c, the change of base formula is:
loga(x) = logc(x) / logc(a)
Usually, base 10 (log) or the natural base e (ln) are chosen because they are most commonly available on calculators.
For example, to compute log2(8) using base 10, you would calculate log10(8) / log10(2).