Recall that we define the logarithm of base 10 of x is the exponent needed to produce x. The equation
means , where .
Logarithms to the base 10 are called common logarithms. Most times, is written as . In this post, we prove that
Let and let . Using the definition above, we have .
By the law of exponents, .
Getting the logarithm of each side, .
By the definition we have mentioned above, .
Substituting to and substituting to , we have