Advanced Fun with Logs

Expand/Condense (must be simplified)

100

log₃x - 3log₃y - 5log₃z

log₃  x/(y³z⁵)

200

log₅(4x²z³/w⁶)

log₅4 + 2log₅z - 6log₅w

300

log(10x⁴)

1 + 4log(x)

400

3ln x + 4ln y - ln x³ + 5 ln z

ln y⁴z⁵

500

log_b (abc)

log_ba + log_bc + 1

Solving Logs

100

log₇x=3

343

200

ln e⁸

8

300

log₃x + log₃(x-2)=1

3

400

log₂(x²-2)=1

2 or -2

500

ln (x²-8)=2

+ or - the square root of e²+8

Growth and Decay

100

$7,300 at 7% compounded semiannually for 3 years

$8,973.56

200

$130 at 9.4% compounded quarterly for 2 years

$156.55

300

You buy a car for $22,500.  The value of the car depreciates by 25% each year.  What is the value of the car after 3 years?

$9,492.19

400

From 1900 to 2000, the population of California can be modeled by P = 29,816,591(1.0218)^t where t is the number of years since 1990.

Estimate the population in 2007

37,013,552

500

An adult takes 400 mg of ibuprofen.  Each hour, the amount of ibuprofen in the person's system decreases by about 29%.  How much ibuprofen is left after 6 hours?

51.42 mg

Convert to a Logarithm

100

Convert to a logarithm: 2⁴=16

log₂16=4

200

Convert to a logarithm: 8²=64

log₈64=2

300

Convert to a logarithm: e^x=8

ln 8 = x

400

Convert to a logarithm: 10⁴=10,000

 log10,000=4

500

Convert to a logarithm and then solve for x: 2^x=1024

 log₂1024=x x=10

Misc.

100

What is the inverse of f(x)=9^x

 f^-1(x)= log₉x

200

What is the sin^-1(sin(7pi/6))  [in radians]

-pi/6

300

What is the name of Mr. Fogelson's dog?

Emma

400

Why does Mr. Fogelson love math

it makes people cry

500

What is the main instrument Mr. Fogelson's son plays in the band NBTF?

Drums