Logarithms Review

Conversion

100

log₅125

2

200

log(x)=4x

10^4x=x

300

log₁₀00.0001=-4

10^-4=00.0001

400

log_(x+5)4x=32

(x+5)³²=4x

500

ln(3x+15)=x-25

e^x-25=3x+15

Condensing and Expanding

100

ln(sl/7)

ln(s)+ln(l)-ln(7)

200

log₆(7/s)

log₆7-log₆s

300

clog4 + ulog7

log(4^c7^u)

400

2log43 - 13log2

log(43²/2¹³)

500

log^2t(sqrt(f))/5d²

log2+logt+1/2logf-log5+2logd

Solving

100

log₂(x-3)=8

259

200

log₂₍(x+3)(3))=log₂27

6

300

log₂(x+2)+log₂(3)=log₂(27)

7

400

log₃(x)+log₃(x-2)=log₃(x+10)

5

500

log₅(x+2)-log₅(x)=log₅(2x-1)-log₅(3x-12)

-3 or 8

Evaluating

100

log₄1/64=

-3

200

log₄58=

2.93

300

log₂₀1200=

2.4

400

log₄0.000002

-9.47

500

log₂₈10⁶

4.15

Miscellaneous

100

What does ln represent?

Natural log, log base e

200

What does log with no visible base mean?

Base is 10

300

What are the properties of logs?

Product, Quotient, Power

400

Why are logs important?

Can condense larger numbers; used in calculus; etc.

500

Who is the best math teacher?

Ms. Watts