Math 3 - Logs/Exp Review

Inverses

100

Find the inverse of:  f(x) = 2^x

f^-1(x) = log₂x

200

Inverse of:   f(x) = ln x

f^-1(x) = e^x

300

Inverse:  f(x) = 3^x - 2

f^-1(x) = log₃(x + 2)

400

f(x) = 3 log (x + 1) - 2

f^-1_{(x) =} 10^(x+2)/3  - 1

500

What is the asymptote of the inverse of:  ln (x - 1) + 3 ?

y = 1

Word Problems

100

Write the function:  $100 grows at 3%

y = 100 (1.03)^x

200

Describe the rate?   y = 900(0.68)^x

Down by 32% per year

300

Yearly growth rate? Year 1:   1800   Year 5:  3600

18.9% or 19%

400

How long will it take for $200 to grow to $600 if the interest rate is 10%?

11.5 years

500

How long would it take to lose half your weight if you lost 15% per year?

4.3 years

Solve this!

100

log₄(4x - 1) = log₄ (x + 5)

x = 2

200

e^{x + 1} = 2

x = -0.31

300

2 + 3^x = 8

x = 1.63

400

log₂(x - 1) + log₂(x + 1) = 3

x = 3

500

log₃(x) + log₃(x - 1) - log₃(x + 1) = log₄1

x = 2.41

I love numbers!

100

log₂8

3

200

log₁₆2

x = 1/4

300

log₂₅(1/5)

x = -1/2

400

ln e²⁰¹

201

500

3 log₂₇81 + 6 log₃₆6

7

Randomness

100

What is the y-int?     f(x) = 1/4 (4) ^x

(0, 1/4)

200

What is "e" to the nearest thousandth?

2.718

300

Which has a faster rate of change?    y = 4(2)^x  OR  y = 4 (1/2)^x

They're both the same.

400

2 log x - 4 log y + 5 log z - 8 log a

log( x²z⁵ / y⁴a⁸ )

500

Make up your own word problem:  y = 500(1.2)^x     

(you cannot use money)

Answers will vary