Unit 4 Review

Exponents -> Logs

100

Exponential functions and logarithmic functions are _________.  

inverses

200

log₃ 27

x = 3

300

log₆ 7776

x = 5

400

Between which two consecutive integers must log₄ 57 must lie?

2 and 3

500

Write 5^-4 = 1/625 in logarithmic form

log₅ (1/625) = -4

Graphs of Logs

100

What is the domain of the function y = log₆ (2x + 8)

(-4, ∞)

200

What is the domain and range of the function log₉(3x - 18)? 

Domain: (6, ∞) Range: (-∞, ∞)

300

What is the domain, range, and equation of the asymptote of the following function log₂(1/2x + 5)?

Domain: (-10, ∞), Range: (-∞, ∞), Asymptote: x = -10

400

What is the domain, range, x-intercept, y-intercept, and equation of the asymptote of the following function f(x) = 4log(x + 7)?

Domain: (-7, ∞), Range: (-∞, ∞), Asymptote: x = -7, X-Intercept: (-6, 0), Y-Intercept: (0, 3.38)

500

What is the domain, range, x-intercept, y-intercept, describe the end behaviors, and equation of the asymptote of the following function f(x) = 1/3log(2x - 5)

Domain: (2.5, ∞), Range: (-∞, ∞), Asymptote: x = 2.5, X-Intercept: (3, 0), Y-Intercept: N/A, x -> 2.5⁺ f(x) -> -∞, x -> ∞ f(x) -> ∞

Laws of Logs

100

Expand: log₂(8x⁴)

3 + 4log₂(x)

200

Condense: 2log(a) + log(b) - 3log(c)

log(a²b/c³)

300

Expand: ln(x³√y/z) 

3ln(x) + 1/2ln(y) - ln(z)

400

Condense: 1/2log₅(x) - (2log₅(y) + log₅(z))

log₅(√x/y²z)

500

Expand: log(∛(a²(a+1)/b⁵))

1/3(2log(a) + log(a+1) - 5log(b)) OR 2/3log(a) + 1/3log(a+1) - 5/3log(b)

Solving Exponentials with Logs

100

2(3^x) = 26

x = 2.34

200

4^x + 9 = 40

x = 2.48

300

3(2^x) - 7 = 14

x = 2.81

400

50 - 5(3^x) = 10

x = 1.89

500

2(6^{x - 1}) - 5 = 18

x = 2.36

Solving Exponentials with Ln

100

e^x = 55

x = 4.01

200

4e^x - 9 = 19

x = 1.95

300

e^{2x + 4} = 10

x = -0.85

400

3e^x + 5 = 29

x = 2.08

500

-2e^{x - 4} + 10 = 2

x = 5.39