Positive real numbers a and b have the property that p p plog a + plog b + log a + log b = 100 and all four terms on the left are positive integers, where log denotes the base-10 logarithm. What is ab? …

The trick to solving a problem like this is to rewrite the number being put into the logarithm — in this problem, 81 — as an exponential whose base is the same as the base of the logarithm — in this …

(Logarithm of One): log b(1) = 0. (Logarithm of b): log b(b) = 1. (Product Law for Logarithms): log b(xy) = log b(x) + log b(y). (Quotient Law for Logarithms): logb(x=y) = logb(x) logb(y).

Exclude from the solution set any proposed solution that produces the log of a negative number or the log of 0. the怍 = log −1 does not work since it produces of a negative怍 = 3 number. Therefore, the …

So if you want to estimate the logarithm of a number, all you have to do is count its digits. For example the number 83,176,000 has eight digits, and therefore its log must be between 7 and 8.

2 Parts of a Logarithm Logarithms generally have the form log b(a) argument. Note that logarithms can have any number as a base. Although this is the general form for a logarithm, sometimes you may …

In this guide, you will learn the definition of a logarithm, the laws concerning logarithms, what the natural logarithm is and finally, how to change the base of a logarithm.