Base e Answers
Identify the graph of y = ln x + 1.
ln e3 =
ln 16 - ln 8
Which expressions are equivalent to 2 ln a + 2 ln b - ln a? Check all that apply.
Question text not available
ln (2x)4 4 ln 2 + 4 ln x4 ln 2 + ln x 8 ln x
Solve: 4 ln x = 2 ln 25x = 5x = 25x = 625
Identify the solution set of 3 ln 4 = 2 ln x.{6}{-8, 8} {8}
Identify the error in the student solution shown below. Find the correct 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.
Identify the graph of y = ex - 2.
Identify the graph of y = ln x + 1.
0✔ 3e3e
ln 16 - ln 8
Which expressions are equivalent to 2 ln a + 2 ln b - ln a? Check all that apply.
ln 3x = 3 ln xln 3 - ln x✔ ln 3 + ln x
4 ln 2 + 4 ln x4 ln 2 + ln x 8 ln x
Solve: 4 ln x = 2 ln 25
Identify the solution set of 3 ln 4 = 2 ln x.
Question text not available
ln 2 + ln 8 - ln 4
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
=
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
Solve: 3 ln x = ln 216x = 3x = 6 x = 72
02 + y2ye✔ 2y
ln 2 + ln 8 - ln 4
Which expressions are equivalent to ln x + 2 ln 5 + ln 1? Check all that apply.
= ✔ ln 2 + ln a - ln bln 2 - ln a - ln b 2 ln a - ln b
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
Identify the solution set of 6 ln e = eln 2x
Which did you include in your solution?
eln 1 = eln 5x =
-10✔ 1e
Question text not available
05 + x5ex✔ 5x
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