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expanding logarithms problem

100

log₅(xy²)⁶

6log₅x+12log₅y

200

log₂(10²/7)⁶

12log₂ 10-6log₂7

300

log8x

log2³+logx=3log2+logx

400

In u²/v⁶

2In u-6In v

500

log3/11

log3-log11

condensing logarithms problem

100

3log₆x-18log₆y

log₆ x³/y¹⁸

200

20log₅u+5log₅v

log₅(v⁵u²⁰)

300

5log₅2-25log₅7

log₅ 2⁵/7²⁵

400

4In x-3In y

In x⁴/y³

500

3In u+2In v

In(v²u³)

solving logarithmic equations

100

6^3x-1=6^-2x

1/5

200

log₁₄(-36+3x²)=log₁₄(4x²-13x)

[4, 9]

300

log₅1/125 

-3 

400

-3log₄9v=-6

16/9

500

log₁₅-5x=log₁₅x

no solution 

Word Problems

100

In 10th grade, you won a scholarship of $500. Your parents deposit in an account for you to use when you go to college. If the account pays 6% annual interest, how much would you have saved when you graduate high school?

$631.24

200

the population of bluefish in Spring Lake was 35,000 in 1990. The population has decreased at 2.7% over time. How many fish would be left in 2019?

15,824 fish

300

A population of 120,000 grows 1.2% per year for 15 years.

144,000 people

400

1. You put $2000 into a college savings account that pays interest at an annual rate of 4%. If you make no additional deposits or withdrawals from the account, how much will be in the account after 3 years? 

$2860

500

Mr. Gandolfi stayed home sick with the flu. He took 300 mg of DayQuil and layed on the couch. If the medicine in his system decreases at 13% per hour, how much medicine will be in his system after 8 hours?

99mg

Extra.

100

log₆18

1.613

200

In50

3.912

300

log₅y=x

5^x=y

400

-9*19^p-1+7=-45.7

1.6002

500

-6*13^x+6=-45

-5.2144