Chapter 6 Flashcards

inverse function

switch x and y, then solve for y

y = a^x

y = log_a(x)

horizontal line test

inverse of a functions can only cross a horizontal line once to be a true inverse

log_a(x) + log_a(y)

log_a(x*y)

log_a(x/y)

log_a(x) - log_a(y)

logs cannot be __

negative

e = __

2.7…

log_e(x) =

ln(x), natural log

log_a(x)^y

y * log_a(x)

a^log_a(b) =

b

log₁₀(1000) =

3

log₁₀(100) =

2

log₁₀(10) =

1

inverse y = e^3x

x = e^3y → log_e(x) = 3y → ln(x)/3 = y

log(100^3x) =

log(10^{2 × 3x}) → log(10^6x) → 6x