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
