LOGS

Condense or expand logs

100

3log₉ 2 − 2log9 5 

log₉ (2³/5²)

200

log₅ (a² /b³)

3log₇ 2 − 2 log₇ 5

300

log₄ (12(7²) ⁴

4 log₄ 12 +8 log₄ 7

400

log base 2 of 3 cubed divided by 7 to the 12. 

3 log₂2 - 12log₂7

500

log base 2 of 5 plus log base 2 of 6 all divided by 2 plus log base 2 of 11 all divided by 2

log₂(5 sqrt 66)

Solving Logs

100

log_x(64+3)

x=4

200

log₄(0.25)=x

x= -1

300

log₄(2x-1)= log₄(16)

x=17/2

400

12^x=18

x= 1.1632

500

3^2x=27

x= 3/2 

Exponential form to log form

100

log₃27= 3

3³= 27

200

log₄16= 2

4²= 16

300

log(1/100)= -2

10^-2= 1/100

400

log₈(4096)=4

8⁴= 4096

500

log₇₉(493,039)=3

79³= 493039

Log form to exponential form

100

3³⁼27

log₃(27)=3

200

2⁵=32

log₂(32)=5

300

8³=512

log₈(512)= 3

400

5^-3= 1/125

log₅(1/125)=-3

500

6^-4=1/1,296

log₆(1/1,296)= -4

Interest

100

$4,000 is invested at 6% compounded quarterly. What is the total after 8 years?

$6,441.30

200

$1,000 is invested at 9% compounded monthly. What is the total after 9 years?

$2,241.12

300

$5,000 is invested at 8% compounded continuously for 5 years. What is the total amount?

$7,459.12

400

What equation do you use to find the half-life?

y=n(1/2)^t/a

a= half life

500

What formula do you use to find compound interest? What formula is used when finding continuous interest?

Compound:

A= P(1+r/n)^nt

Continuous:

A= Pe^rt