Quotient Rule

log_aM/N = log_aM - log_aN

log_aMN = log_aM + log_aN

Power Rule

log_aM^P = plog_aM

Inverse Rules

1. log_aA^x = x

2. a^log_aX = x

y=log_ax <=> a^y=x

If there is no 'a', the base of log is understood to be 10

ln_ex <=> ln x

If no base, it is understood to be "e"

ex: log_b1/8=y
8^y=1/8

y= -1

if there is a fraction, the exponent is a negative

EXAMPLE

Log_ab=c

a^c=b

ln_e1/e⁴= -4

e^-4= 1/e⁴

To Graph, it MUST be in Exponential form

y=2log₂x

log₂x=y

2^y=x

x³ * x⁵ = x⁸

x³ + x⁵ = x⁸

(x³)⁵ = x¹⁵

Change of Base

log_bm= ^log_am/log_ab

where a is understood to be 10

*use calculator

Example:

log₅x=3

5³=x

x=125

*** x can NOT be a negative number ***

A = P(1 + ^r/_n)^nt

A - Amount $ After Investment
P = Amount Invested

r = Interest Rate

n = # of times compounded in a year

t = time (years)

A = Pe^rt

A - Amount $ After Investment
P = Amount Invested

e = use calculator

r = interest rate

t = time (years)

P(t) = P0e ^kt

k = constant rate of growth (+) or decay (-)

P(t) = ending amount
P0 = Intital Amount
e = use calculator

Difference of Cubes

a³-b³=(a-b)(a²+ab+b²)

Sum of Cubes

a³+b³=(a+b)(a²-ab+b²)

Using Properties of Logarithmic Functions to Expand OR Decrease and Expression

(Quotient, Product, Power, Inverse)

To Expand:

Quit Peeing In then Pool

To Decrease/Condense:

Pee In Proper Quarters