
Log _{x} ab = log _{x} a + log _{x} b. Proof: log _{x} ab = p, therefore ab = x^{p}I Let log _{x} a = q, a = x^{q}II log _{x} b = r, b = x^{r}III From I and II, ab = x^{q}.x^{r} = x^{q+r} from I, ab = x^{p}IV from I, II, III and IV, we get x^{p} = x^{q+r} Therefore, p = q + r Therefore, log _{x} ab = log _{x} a + log _{x} b The logarithm of the product of two numbers is equal to the sum of the logarithms of those to numbers.
Example: Directions: Solve the following problems. Also write at least five examples of your own. 