Intro to Logarithms Review

Condense and Expand Logarithms

100

Rewrite log₆36=2 in exponential form

6²=36

200

Rewrite log₄(1/4)=-1

4^-1=1/4

300

Rewrite log₂₈₉17=1/2 in exponential form

289^1/2=17

400

Rewrite log_(1/2)8=-3 in exponential form

(1/2)^-3=8

500

Rewrite log_(7/4)x=y in exponential form

(7/4)^y=x

Solving Without a Calculator

100

Solve for x: 4^x = 16

x = 2

200

log₅125

x = 3

300

log_(1/4)64

x = -3

400

log₃₄₃7=x

x= 1/3

500

log₆ (1/216) = x

x=-3

Rules of the Log

100

log₆x=2

What is 36?

200

log₄x=-2

What is x=(1/16)

300

log₈₁x=(1/4)

x= 3

400

log_(1/625) x = (-1/2) 

x= 25

500

log₆ x+2=3 

x = 214

Solving With a Calculator

100

log_x64 = 3

x = 4

200

log_x8= 3

x = 2

300

log_x(1/4)= -2 

x =2

400

log_x(125/27)=(3/4)

x = 625/81

500

log_x8 = (3/5)

x= 32

Compound Interest

100

Convert to log form: 5² = 25 

log₅25=2

200

Convert to log form: 6^-2=1/36

log₆(1/36)=-2

300

Convert to log form: (1/4)^-2=16

log_(1/4)16=-2

400

Convert to log form: 32=2⁵

log₂32=5

500

Convert to log form: 81=3^x+1

log₃81=x+1