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Chp 6 Exponential and Logarithmic Functions (Logarithmic Functions # #…
Chp 6 Exponential and Logarithmic Functions
Logarithmic Functions
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Converting, find base first
Switch x and y
Solve for y
isolate log
Switch to exp form
Graphing
Flip over y = x
Switch x and y for existing coordinates
3 points always exist
Transformations
-log, -ln; flip over x-axis
Differentiate between outside/inside arg
Properties
Requires positive base and arg x
Domain: (0,∞) Range: (-∞,∞)
Inverse of exp form
Base a ≠ 1, a > 0
|x| allows base to be (-∞,∞) ≠ 0
Log types
Common, base 10
Natural, base e
written with ln instead of log
Solve Log eq for x
Check a ≠ 1
Switch to exp/log form if necessary
Check that solutions are positive for base
Use ln button (calculator) for log solving
Exponential Functions
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Properties
Base a, growth factor
Base a ≠ 1, a > 0
Forms: f(x) = Ca^x
x = a^y
Initial Value, C
Domain: (-∞,∞) Range: (0,∞)
Solve for x
Switch to log form if necessary
Build Exp function
Base a is consecutive ratio output
Find from quotient of consecutive output, y
Initial value c, use f(0)
Graphing
3 points always exist
a > 1, normal exp function
0<a<1, decreasing
flipped over y?
Transformations
Differentiate between outside/inside arg
(-) base a ; flip over x-axis
Number e
log function
Form: y = ln x
Exp function
form: explicit, y = e^x
Inverse