Precalc Logs Review

Exp to Logs

100

3³ = 27

log₃27 = 3

200

12^x=144

log₁₂144 = x

300

e⁴=y

ln y = 4

400

2^3-x = 64

log₂64 = 3-x

500

10^2y = 10000

log 10000 = 2y

Logs to Exp

100

log₂32=5

2⁵=32

200

log_x2z=y

x^y=2z

300

log 1000 = 3

10³=1000

400

log₃(2y) = x+3

3^x+3=2y

500

ln 1 = 0

e⁰ = 1

Laws of Logs

100

log₂z⁴

4log₂z

200

log₂(xy)

log₂(x) + log₂(y)

300

log₃9x⁴

4log₃9 - 4log₃x

400

log₂(x³/y)

3log₂x - log₂y 

500

log₅5^p

p

Exp/Log Equations + Word Problems

100

ln(2+x) = 1

x = 0.718

200

10^6-3x=2

x = 31.333 

300

4 + 3log(2x) = 16

x = 5000

400

The velocity of a sky diver t seconds after jumping is given by: 

v(t) = 80(1-e^-0.2t)

After how many seconds is the velocity 60 ft/s? (Round to 2 decimal places)

6.93 seconds

500

In a certain lake the intensity of light (given by "I") at depth "x" is given by :

I = 10e^-0.008x 

What what depth has the light intensity dropped to I = 5?

86.64 ft