Log and Exponential Review Alg 2

Like Bases

100

Solve for x

2^(4x)=2

x=1/4

200

3^(x-1)=81

x = 5

300

1/2=8^(x-5)

x=14/3

400

16^(2x)=4^(x+2)

x=2/3

500

(1/2)^(x-5)=(1/4)^x

x=-5

Evaluate logs

100

log₂ 4

2

200

log₃ 81

4

300

log 1000

3

400

log(sqrt10)

1/2

500

log₈ (1/64)

-2

Expand logs

100

log₅(xy)

log₅ x + log₅ y

200

log_3 (x/y^2) 

log₃ x - 2log₃ y

300

log_{6  sqrt x} 

1/2 log₆ x

400

log₈   (4xy^2)^2 

log₈ 16+2log₈ x+4log₈ y

500

log  sqrt((xy)/z) 

1/2(log x +log y -log z)

Mixed

100

Solve to three decimal places 

2.8^(x)=41

x=3.607

200

Condense:

2log₅ x - 6log₅ y - 2log₅ z

log₅

(x^2/(y^6z^2))

300

Round to 2 decimal places

 2^x-7=7 

x =3.81

400

Solve:

2^(3x-4)=1/32

x=-1/3

500

log₈ (4x+4)=2

x=15

Solve log equations

100

log₅ (2x+3)=log₅ (5x-1)

x=4/3

200

log₇(x+6)=2

x=43

300

log 10 - log x = log 50

x=1/5

400

log₆ x +log₆ (x-5)=2

x = 9

500

log (x-1) - log (x-2) = log 5

x=9/4