AP Precalc 2.9 - 2.13

log/ln multiplied can be split up into

addition

log/ln divided can be split up into

subtraction

log/ln with an exponent moves to

front of the log/ln

log_b x can be evaluated as

ln x/ln b

changing log to exponential form, example: log₂ (4x) = 5

4x = 2⁵

changing exponential to log form, example:

8^x-3 = 26

log₈ 26 = x-3

changing e to ln, example: e^x = x^1+x

“ln both sides,” x= ln x^1+x

how to solve quadratic type equations

let u = e^x

if looking at inequalities and the base of the log or exponent is less than 1, you have to

flip the inequality sign

how to find values of logs, example: log₉ 27

“9^? = 27,” change bases to the same,

so (3² )^a = 3³ , then 2a=3 and solve.

negative exponents are the

reciporical, ex 2^-1 = 2

fraction exponents are

the root, 8^2/3= ³√8² = 2² = 4

when asked to find values of x for which f(x) is less/greater than a number, you need to

create a number line using solutions

log shape

goes up and to the right, usually with asymptote x=0

find the inverse of logs

switch x and y, will convert to exponential function

x-axis reflection

negative in front of entire equation

y-axis reflection

negative in front of x in the parentheses

vertical dilation

number in front of entire equation, stays the same

horizontal dilation

number in front of x in parentheses, turns into reciporical, ex 2 = 1/2

find domain of logs

put whats in parentheses in front of “greater than 0)

end behaviors of logs

one side will always go towards vertical asymptote, other side will always go towards infinity/ negative infinity