4.2 Logarithms

b is the base y is the exponent (can be all real numbers) b CANNOT = 1 b must always be greater than 0 X is the argument – must be > 0 “log b x is the exponent to which the base b must be raised to give you x.”

Write in the other form: 3 2 = 9 log = 3

Properties log a 1 = 0 log a a = 1 log a a x = x

Evaluate: log ,000 log 16 4 log 5 1 log 5 5 8

Solve for the variable. log b 9 = 2

Log functions and exponential functions are inverses of each other. Since the domain of an exponential is all real numbers and the range is y > 0, then for:

Graph: y = log 2 x

Explain the graphs of: y = -log 2 x y = log 2 (-x) Reflect across the x-axis Reflect across the y-axis

y = -log 2 xy = log 2 (-x)

Common Logarithms – base 10 logx = log 10 x Natural Logarithms – base e lnx = log e x y = lnx is the inverse of y = e x

Simplify log 4log 0.1 ln 1ln e ln e 8 ln 5

Explain the graphs and find the domain. y = 2 + log 5 x y = log 10 (x – 3) y = ln (4 – x 2 ) Shift vertically up 2 Shift horizontally right 3

Homework pg 349 #3-37 odd, all