Answers SS4 PGCPS ALGEBRA 2 OC SUMMER 2027 - 793033Base e

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Identify the graph of y = ex - 2.

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Identify the graph of y = ln x + 1.

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Answers:

ln e3 =:3

ln e2y =:2y

ln e3 =

2 + y

2ye

ln 16 - ln 8

ln 2

ln 8

ln 128

Which expressions are equivalent to 2 ln a + 2 ln b - ln a? Check all that apply.

ln ab2 - ln a

ln a + 2 ln b

ln a2 + ln b2 - ln a

2 ln ab

ln ab2

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ln (2x)4 4 ln 2 + 4 ln x4 ln 2 + ln x 8 ln x

4 ln 2 + 4 ln x

4 ln 2 + ln x

8 ln x

Solve: 4 ln x = 2 ln 25x = 5x = 25x = 625

x = 5

x = 25

x = 625

Identify the solution set of 3 ln 4 = 2 ln x.{6}{-8, 8} {8}

{6}

{-8, 8}

{8}

A town predicts that its population will double in years.Simplify the expression. In how many years will the population of the town double?

Answer:

Identify the graph of y = ex - 2.

Option

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ln e3 = ln e2y =

Answers:

Selection 1:3

Selection 2:2y

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4 ln 2 + 4 ln x

4 ln 2 + ln x

8 ln x

Solve: 4 ln x = 2 ln 25

x = 5

x = 25

x = 625

Identify the solution set of 3 ln 4 = 2 ln x.

{6}

{-8, 8}

{8}

A town predicts that its population will double in years.Simplify the expression. In how many years will the population of the town double?

Answer:

Identify the error in the student solution shown below. Find the correct answer.

Answer:

The error in the student's solution is the attempt to apply the quotient property of logarithms to the constant 0. Since 0 is not a logarithm, the expression ln(3x) - 0 cannot be written as a quotient of logarithms; it simply simplifies to ln(3x). Correct solution: ln(x^2) = ln(3x) x^2 = 3x x^2 - 3x = 0 x(x - 3) = 0 x = 0, x = 3 Since the domain of a natural logarithm is x > 0, x = 0 is an extraneous solution. The correct answer is x = 3.

02 + y2ye✔ 2y

2 + y

2ye

ln 2 + ln 8 - ln 4

ln 4

ln 6

ln 64

Which expressions are equivalent to ln x + 2 ln 5 + ln 1? Check all that apply. 2 ln 5xln (x + 26)ln 25x + ln 1ln 25x

2 ln 5x

ln (x + 26)

ln 25x + ln 1

ln 25x

ln 2 + ln a - ln b

ln 2 - ln a - ln b

2 ln a - ln b

ln 4y5 x2 ln 4 - 2 ln x - 5 ln y ln 4 - 2 ln x + 5 ln y -8 ln x + 5 ln y

ln 4 - 2 ln x - 5 ln y

ln 4 - 2 ln x + 5 ln y

-8 ln x + 5 ln y

Solve: 3 ln x = ln 216x = 3x = 6 x = 72

x = 3

x = 6

x = 72

Identify the solution set of 6 ln e = eln 2x{2}{3}{6}

{2}

{3}

{6}

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Which expressions are equivalent to ln x + 2 ln 5 + ln 1? Check all that apply.

2 ln 5x

ln (x + 26)

ln 25x + ln 1

ln 25x

ln 2 + ln a - ln b

ln 2 - ln a - ln b

X 2 ln a - ln b

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ln 4 - 2 ln x - 5 ln y

ln 4 - 2 ln x + 5 ln y

-8 ln x + 5 ln y

Solve: 3 ln x = ln 216

x = 3

x = 6

x = 72

Identify the solution set of 6 ln e = eln 2x

{2}

{3}

{6}

Which did you include in your solution?

Since 0 in ln(3x) - 0 is not a logarithm, the property of logarithms cannot be used here.

The difference shown cannot be written as a quotient of logarithms.

The step ln(x2) = ln(3x) - (0) reduces to ln(x2) = ln(3x).

The possible solutions are 0 and 3, with 0 being extraneous.

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Answers:

eln 1 =:1

eln 5x =:5x

eln 1 = eln 5x =

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05 + x5ex✔ 5x

5 + x

5ex

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