Base e

Question 1

4 ln 2 + 4 ln x4 ln 2 + ln x 8 ln x

Revolt · Accepted Answer

4 ln 2 + 4 ln x

Question 2

Solve: 4 ln x = 2 ln 25

Revolt · Accepted Answer

x = 5

Question 3

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

Revolt · Accepted Answer

{8}

Question 4

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

Revolt · Accepted Answer

5

Question 5

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

Revolt · Accepted 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.

Question 6

Which did you include in your solution?

Revolt · Accepted Answer

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.

Question 7

ln 2 + ln 8 - ln 4

Revolt · Accepted Answer

ln 4

Question 8

= ln 2 + ln a - ln bln 2 - ln a - ln b 2 ln a - ln b

Revolt · Accepted Answer

ln 2 + ln a - ln b

Question 9

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

Revolt · Accepted Answer

ln 4 - 2 ln x + 5 ln y

Question 10

Solve: 3 ln x = ln 216

Revolt · Accepted Answer

x = 6

Base e Answers

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