4.2 Logarithms
b must always be greater than 0 y is the exponent X is the argument b is the base b CANNOT = 1 b must always be greater than 0 y is the exponent can be all real numbers X is the argument must be > 0 “logbx is the exponent to which the base b must be raised to give you x.”
Write in the other form: 32 = 9 log 6216 = 3
Properties loga1 = 0 logaa = 1 logaax = x
Evaluate: log10100,000 log164 log51 log558
Solve for the variable. logb9 = 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 = log2x
Explain the graphs of: y = -log2x y = log2(-x) Reflect across the x-axis Reflect across the y-axis
y = -log2x y = log2(-x)
Common Logarithms – base 10 logx = log10x Natural Logarithms – base e lnx = logex y = lnx is the inverse of y = ex
Simplify log 4 log 0.1 ln 1 ln e ln e8 ln 5
Explain the graphs and find the domain. y = 2 + log5x y = log10(x – 3) y = ln (4 – x2) Shift vertically up 2 Shift horizontally right 3
Homework pg 349 #3-37 odd, 41-46 all