Base e Answers
Identify the graph of y = ex - 2.
Identify the graph of y = ln x + 1.
ln e3 =
Question text not available
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 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.
Identify the error in the student solution shown below. Find the correct answer.
The error occurs in the last step where the student applied the quotient property of logarithms incorrectly. The term '0' is a scalar value, not a logarithm, so the property ln(a) - ln(b) = ln(a/b) does not apply. Instead, the equation ln(x^2) = ln(3x) - 0 should simply be simplified to ln(x^2) = ln(3x). To find the correct solution: 1. Solve ln(x^2) = ln(3x) by setting the arguments equal: x^2 = 3x. 2. Rearrange the equation: x^2 - 3x = 0. 3. Factor: x(x - 3) = 0. 4. Solutions are x = 0 and x = 3. 5. Check for extraneous solutions: The original equation contains ln(x), and the argument must be positive (x > 0). Therefore, x = 0 is extraneous. 6. The final correct solution is x = 3.
Which did you include in your solution?
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. 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
Question text not available
eln 1 = eln 5x =
-10✔ 1e
05 + x5ex✔ 5x
05 + x5ex✔ 5x
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