Base e Answers
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?
Identify the graph of y = ex - 2.
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
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
-101e
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