Logarithms

Converting

100

Convert the log equation to an exponential equation

log₃9 = 2

3² = 9

200

Convert the log equation to an exponential equation

ln(x) = 58

e⁵⁸ = x

300

Convert the log equation to an exponential equation

ln(x - 9) = 32

e³² = x - 9

400

Convert the exponential equation to a log equation 

14² = 196

log₁₄(196) = 2

500

Convert the exponential equation to a log equation 

2^-3 = 1/8

log₂(1/8) = -3

Condensing

100

Condense the logarithm

5 × log₂

log₂⁵

log₃₂

200

Condense the logarithm

log₂7 + log₂4

log₂28

300

Condense the logarithm

log₃15 - log₃15

log₃1

0

400

Condense this logarithim

log(x²) - log(y³)

log(x²/y³)

500

Condense this logarithim

4 ln(x+6) - 3 ln x

ln(x+6⁴/x³)

Evaluating

100

Evaluate the logarithm

log₂32 = x

x = 5

200

Evaluate the logarithm

log₇(1/4) = x

x = -7

300

Evaluate the logarithm

log₂(1/16) = x

x = -4

400

Evaluate the logarithm. Round to the hundredth place.

log₇35 = x

x = 1.83

500

Evaluate the logarithm. Round to the hundredth place.

log₅38 = x

x = 2.26

e and ln

100

−5 * e−x + 2

− ln (2 − x/5)

200

1 − 2e^-2x

1/2 ln (1-x/2)

300

ln(x-9) = 32

e³²= x-9

400

10e^x/2 = 1

-4.61

500

228e^x/4 = 76

-4.39

Applications

100

John bought a truck for $22,350, but it has depreciated at a rate of 8.5% since he bought it. If it's now worth $14,344.51, how long has he owned the truck?

~5 years

200

A virus is spreading at a rate of 4.5% per day. Currently there are 300 people infected, about how long will it take for there to be 1000 people infected?

~28 days

300

A video posted on YouTube initially had 80 views as soon as it was posted. The total number of views to date has been increasing exponentially according to the exponential growth function y=80e^.12t represents time measured in days since the  video was posted. How many days does it take until 2500 people have viewed this video? 

~28.7 days

400

After taking a cough suppressant, the amount, A, in mg, remaining in the body is given by A = 10(0.85)^t, where t is given in hours. How long will it take to have only 1 mg left in the body?

~14 hours

500

Kelly invests $5000 with a bank. The value of her investment can be determined using the formula y = 5000(1.06)^t, where y is the value of the investment at time t, in years. Approximately how many years will it take for Kelly's investment to reach $20,000?

~23.8 years