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Use the Properties of Logarithms to Expand the Expression as a Sum

Question 3

Multiple Choice

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
lnxx233\ln \frac { x } { \sqrt [ 3 ] { x ^ { 2 } - 3 } }


A) lnx+23ln(x3) \ln x + \frac { 2 } { 3 } \ln ( x - 3 )
B) 13lnx+ln(3) \frac { 1 } { 3 } \ln x + \ln ( - 3 )
C) 13lnxln(3) \frac { 1 } { 3 } \ln x - \ln ( - 3 )
D) lnx23ln(x3) \ln x - \frac { 2 } { 3 } \ln ( x - 3 )
E) lnx13ln(x23) \quad \ln x - \frac { 1 } { 3 } \ln \left( x ^ { 2 } - 3 \right)

Correct Answer:

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