Stitz-Zeager_College_Algebra_e-book

2 here a 2 and b e so we have 2x ex ln2 to verify

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: e called ‘logs’ for short. Definition 6.2. The inverse of the exponential function f (x) = bx is called the base b logarithm function, and is denoted f −1 (x) = logb (x) The expression logb (x) is read ‘log base b of x.’ We have special notations for the common base, b = 10, and the natural base, b = e. Definition 6.3. The common logarithm of a real number x is log10 (x) and is usually written log(x). The natural logarithm of a real number x is loge (x) and is usually written ln(x). Since logs are defined as the inverses of exponential functions, we can use Theorems 5.2 and 5.3 to tell us about logarithmic functions. For example, we know that the domain of a log function is the range of an exponential function, namely (0, ∞), and that the range of a log function is the domain of an exponential function, namely (−∞, ∞). Since we know the basic shapes of y = f (x) = bx for the different cases of b, we can obtain the graph of y = f −1 (x) = logb (x) by reflecting the graph of f across the line y = x...
View Full Document

This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online