Algebra 2H Unit 6 Review

Simplifying Logarithmic Expressions

100

Evaluate.

log_64(2)

1/6

200

Evaluate.

e^ln6

6

300

log_9(27)

3/2

400

If 

ln(2) = 0.693

ln(3) = 1.099

Find 

ln(18)

2.891

500

If 

log3 = 0.477, log4 = 0.602, log6 = 0.778

Find 

log(8)

0.903

Solving Exponential Equations

100

Solve. Give an exact answer.

7(4)^(x - 3) = 13

log_4(13/7) + 3

200

Solve. Give an exact answer.

8(20)^(x - 2) + 2 = 71

log_20(69/8) + 2

300

Solve. Give an exact answer.

-3^(4x-5) - 8 = -41

(log_3(33) + 5)/4

400

Solve. Give an exact answer.

4(10)^(-8x - 1) - 2 = 90

(-log23 - 1)/8

500

Solve. Give an exact answer.

-5e^(3x - 9) + 3 = -6

(ln(9/5) + 9)/3

Solving Logarithmic Equations

100

Solve.

log_11(-5x) = log_11(-x + 8)

-2

200

Solve.

log_3(10x + 3) = log_3(x^2 + 12)

x = 1, 9

300

Solve.

-3log_7(-8x - 4) - 4 = -7

x = -11/8

400

Solve. Give an exact, simplified answer.

log_5(7 - 2x^2) + log_5(10) = log_5(60)

x = +-sqrt2/2

500

Solve. Give an exact answer.

ln9 - ln(2-4x) = 1

x = (-9+2e)/(4e)

Graphing Exponential Functions

100

What is the domain and range of 

y = -2^(x) - 2

Domain:

(-oo, oo)

Range: 

(-oo, -2)

200

What are the x and y intercepts of the function

y = -e^(2x) + 3

(ln3/2, 0), (0, 2)

300

What is the end behavior of the function

y = (1/2)^x + 1

x -> oo, f(x) -> 1

x -> -oo, f(x) -> oo

400

Consider the function: 

y = 2(1/2)^(3x + 1) - 5

Transform these three coordinates from the parent function. 

(-1, 2), (0, 1), (1, 1/2)

(-2/3, -1), (-1/3, -3), (0, -4)

500

Consider the function: 

y = -e^(-2x + 4) + 3

Transform the coordinates from the parent function for x = 0, 1, and 2. Write the asymptote equation, domain, range, and x/y intercepts. All answers should be exact!

Coordinates: 

(2, 2), (3/2, -e+ 3), (1, -e^2 + 3)

Asymptote: 

y = 3

Domain: 

(-oo, oo)

Range: 

(-oo, 3)

Intercepts: 

(0, -e^4 + 3) ((ln3 - 4)/-2, 0)

Graphing Logarithmic Functions

100

What is the domain and range of the following function.

y = log(x + 4) - 2

Domain: 

(-4, oo)

Range: 

(-oo, oo)

200

What are the x and y intercepts of the following function?

y = log_4(x + 2) - 5

(0, -9/2), (1022, 0)

300

Describe the end behavior of the following function.

y = log_(1/4)(x - 1) + 8

x -> oo, f(x) -> -oo

x-> 1^+, f(x) -> oo

400

For the function 

y = 3log_(1/2)(-2x + 3) - 7

transforms these coordinates from the parent function:

(1/2, 1), (1, 0), (2, -1)

(5/4, -4), (1, -7), (1/2, -10)

500

For the function 

y = 1/2ln(4x - 8) + 2

Transform these coordinates from the parent function for x = 1, e, and e^2. Then write the asymptote equation, domain, range, and x/y intercepts. 

Coordinates: 

(9/4, 2), (e/4 + 2, 5/2), (e^2/4 + 2, 3)

Asymptote: 

x = 2

Domain: 

(2, oo)

Range:

(-oo, oo)

Intercepts: no y-intercept 

(1/(4e^4) + 2, 0)