Which of the following logarithmic expressions are equivalent to natural log start root x y end root plus natural log left parenthesis start fraction x over e end fraction right parenthesis? Select all that apply.
(2 points)
Responses
natural log left parenthesis start fraction start root x cubed y over e end fraction right parenthesis
Image with alt text: natural log left parenthesis start fraction start root x cubed y over e end fraction right parenthesis
natural log left parenthesis start fraction x squared y over 2 e end fraction right parenthesis
Image with alt text: natural log left parenthesis start fraction x squared y over 2 e end fraction right parenthesis
one half natural log x squared y minus e
Image with alt text: one half natural log x squared y minus e
natural log left parenthesis x start root x y end root right parenthesis minus 1
Image with alt text: natural log left parenthesis x start root x y end root right parenthesis minus 1
Start Fraction 3 over 2 End Fraction natural log x plus Start Fraction 1 over 2 End Fraction natural log y minus 1
Image with alt text: Start Fraction 3 over 2 End Fraction natural log x plus Start Fraction 1 over 2 End Fraction natural log y minus 1
The logarithmic expressions that are equivalent to natural log start root x y end root plus natural log left parenthesis start fraction x over e end fraction right parenthesis are:
- natural log left parenthesis start fraction start root x cubed y over e end fraction right parenthesis
- natural log left parenthesis start fraction x squared y over 2 e end fraction right parenthesis
- natural log left parenthesis x start root x y end root right parenthesis minus 1