Answer to Question #8172 in Algebra for Brian

Question

Why does a scientific calculator have only two keys for calculating logarithms—natural log and common log?

Answer 1

The logarithm log_b(x) can be computed from the logarithms of x and b with respect to an arbitrary base k using the following formula:

log_b(x) = log_k(x)\log_k(b).

Typical scientific calculators calculate the logarithms to bases 10 and e. Logarithms with respect to any base b can be determined using either of these two logarithms by the previous formula:

log_b(x) = log_10(x)\log_10(b) = log_e(x)\log_e(b).