Logarithms

What Property is it?

100

What property would you use to expand?

ln(15/x)

Property 2

200

What properties (in order) would you use to condense?

klog 2 + 3log h

Property 4 --> Property 1

300

What properties (in order) would you use to expand?

log₂(m⁵p³/b)

Property 2 --> Property 1 --> Property 4

P0 - converting - definition

100

Convert into exponential form

log₅ 25 = y

5^y =25

200

Convert into logarithm form

9^{2x + 3} = 81

2x + 3 = log₉ 81

300

Convert

e^{-x + 7} = 32

ln 32 = -x + 7

P1

100

Expand

log₂ xy

log₂ x + log₂ y

200

Condense

log 3m + log 4n

log 12mn

300

Condense

ln (-2x + 3) + ln -4

ln (8x - 12)

P2

100

Expand

log₂ x/y

log₂ x - log₂ y

200

Condense

ln (2 + k) - ln h

ln ((2 + k)/h)

300

Condense

3log y - log(z - 14)

log (y³/(z - 14))

P4

100

Expand

log₂ x^y

ylog₂ x

200

Condense/Simplify

2log_x 3y

log_x 9y²

300

Expand

ln((4³a^-2)/(y + 5))

3ln 4 - 2ln a - ln(y + 5)