]> Exercise 2.14

Exercise 2.14

Deduce from these two equations that for log to any base we have log a b = 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 log c x = ln x ln c .

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.