## Exercise 2.14

Deduce from these two equations that for log to any base we have log ab = log a + log b.

Solution:

Suppose we want to prove this for logarithms to base c. We deduced in the previous exercise that we can write .

Applying this fact to each logarithm here, the result we want to prove is the same result for natural logarithms, with each term divided by ln c.

In other words, the corresponding result for natural logarithms, which we proved in the previous exercise, implies this one on dividing each term by ln c, and using the fact just mentioned.