Evaluating Logarithms
Solving Logarithms
Solving exponentials with logs
Word Problems
Zilban Lore
100

logunderset(12)() (144)

logunderset(12)() (144) = 2

100

logunderset(7)() x = 2

x=49

100

3^x = 9

x= logunderset(3)() 9 = 2

100

If a bank account has $5,000 and accrues 10% interest, how many years until it has $20,000?

(Hint: 1st one is free...  20000=5000(1.10)^t 

frac{20000}{5000}=frac{5000(1.10)^t}{5000}

4=1.1^t

t=logunderset(1.1)()4 approx 14.545

about 15 years.

100

One of the next three countries Zilban wants to travel/visit:

Portugal, Turkey, or Japan

200

logunderset(3)() (81)

logunderset(3)() (81) = 4

200

logunderset(8)() x = frac{1}{64}

x= -2

200

4^(x+3)=16^x

4^(x+3)=(4^2)^x

4^(x+3)=4^(2x)

x+3=2x

x=3

200

A 100g sample of bacteria doubles every hour. How many hours until it is 1,000,000g ?

1000000=100(2)^h

frac{1000000}{100}=frac{100(2)^h}{100}

10000=2^h

h=logunderset(2)()10000 approx 13.2877

about 13 hours


200

Zilban's favorite spring flower

Tulips 

300

logunderset(2)() (frac{1}{32})

logunderset(2)() (frac{1}{32}) = 5

300

logunderset(9)() (x+4) = logunderset(9)() (2x-1)

x=5

300

3^(2x+5)=27^x

3^(2x+5)=(3^3)^x

3^(2x+5)=3^(3x)

2x+5=3x

x=5

300

A fire triples in size every 5 minutes. If a forest fire is 200 acres big today, how long would it take to be 500,000 acres big if unhindered?

500000=200(3)^t

frac{500000}{200}=frac{200(3)^t}{200}

2500=3^t

t=logunderset(3)()2500 approx 7.12

7.12*5 = 35.60 approx 36 min


300

Zilban's favorite Jim Carrey movie

The Truman Show

400

logunderset(5)() 5^7

logunderset(5)() 5^7 = 7*logunderset(5)() 5 = 7*1 = 7

400

ln(x)=1

x= e approx 2.718281828459045

400

8^(x-2) = 2^(x-4)

(2^3)^(x-2)=2^(x-4)

2^(3x-6)=2^(x-4)

3x-6=x-4

x=1


400

Every time you breathe, you keep about 88% of the air in your lungs. How many breaths does it take to have 50% new air in your lungs?

50%=88%^b

0.5=0.88^b

b=logunderset(0.88)()0.5 approx 5.4222

about 5 breaths


400

Name one of Zilban's top 5 favorite cartoons

Simpsons, Samurai Jack, Dragonball Z, Cowboy Bebop, One Piece

500

logunderset(9)() 9^((2x+1)

logunderset(9)() 9^((2x+1)) = 2x+1

500

logunderset(2)() (x+4)+logunderset(2)() (8) = 7

x=12

500

3^x = 62

x= logunderset(3)() 62 approx 3.76

500

Every time you breathe, you keep about 88% of the air in your lungs. How many breaths does it take to have REPLACED 99% of your breath? 

Hint: 100% - 99% = 1%

1% = 88%^b

0.01=0.88^b

b=logunderset(0.88)()0.01 approx 36.024

about 36 breaths



500

Zilban's favorite punk band

DRI

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