Why Use Logarithms?
Suppose we have a very efficient way of writing any number as powers of a fixed number, say 10:
x = 10m
y = 10n
Then we can perform multiplication and division by using addition and subtraction (of exponents):
xy = 10m+n
A logarithm is just another name for an exponent with respect to a certain base such as 10.
Let b > 0.
If y = bx, then we write logb(y) = x or simply logb y = x (read "log of y with base b")
Note: logb y is not defined for y ≤ 0 , as y = bx > 0 for any x (as b > 0).
For this exercise, evaluate the logarithm, to the base shown, of the number.