Exponentials and Logarithms
Exponential Functions
● In the form y = ax
● Often used to model growths → exponential growths take the form y = cakx
● Can also have exponential decays (take the form y = ca−kx )
Courtesy of Mathematics LibreTexts
Logarithms
● Logarithms (logs) are the inverse of exponentials
● log a b = x ⇔ ax = b
● Essentially logs ask ‘what power must I raise a to in order to get b ?’
● Laws of logarithms:
○ log x + log y = log xy
x
○ log x − log y = log y
○ log xn = n log x
○ log a a = 1
Change of Base Rule
Courtesy of Khan Academy
Exponential Functions
● In the form y = ax
● Often used to model growths → exponential growths take the form y = cakx
● Can also have exponential decays (take the form y = ca−kx )
Courtesy of Mathematics LibreTexts
Logarithms
● Logarithms (logs) are the inverse of exponentials
● log a b = x ⇔ ax = b
● Essentially logs ask ‘what power must I raise a to in order to get b ?’
● Laws of logarithms:
○ log x + log y = log xy
x
○ log x − log y = log y
○ log xn = n log x
○ log a a = 1
Change of Base Rule
Courtesy of Khan Academy
