Unit 7 Review

Log to exp. form

100

log₃27=3

3^3=27

200

log₅625=4

5^4=625

300

log₄64=3

4^3=64

400

log₈64=2

8^2=64

500

e⁶=x-2

log_ex-2=6

Exp.to Log Form

100

8²=64

log₈64=2

200

5²=25

log₅25=2

300

2^x-4=32

log₂32=x-4

400

10^2x=54

log54=2x

500

ln x =38

log_ex=38

e³⁸=x

Evaluate Logarithms

100

log₉81

2

200

log₈₁3

CHANGE BASE FORMULA

1/4

300

log₅(1/2)

CHANGE BASE FORMULA

log(1/2)/log(5) = -0.43

400

log63

CHANGE BASE FORMULA

log63/log10 = 1.8

500

ln 42

log_e42=x

CHAGE BASE FORMULA

log42/loge

3.74

Rules

100

3*log 2

Power Rule:

log 2³

log 8

200

log₃(x-2)+log₃(3)

PRODUCT RULE

log₃(x-2)*3

log₃3x-6

300

log₅85-log₅5

QUOTIENT RULE

log₅(85/5) = log₅17

400

3*log 2 + log (x-4)

POWER AND PRODUCT RULE

log 2³+log (x-4)

log 8 + log (x-4)

log 8(x-4)

log 8x-32

500

Expand the expression:

log(xy/z)

log xy - log z

Log Equations

100

log₄(5x+7)=log₄(2x+31)

x=8

200

log₂(9m+2)=7

2⁷=9m+2

128=9m+2

126=9m

m=14

300

8^n-5=48

log₈48=n-5

1.86 = n-5

n=6.86

400

7¹⁰ⁿ+2=81

7¹⁰ⁿ=79

log₇79=10n

2.25=10n

n=2.25/10 or 0.225

500

What's Ms. Vargas favorite color?

Pink :)