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

Question 70

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.)
lnxx523\ln \frac { x } { \sqrt [ 3 ] { x ^ { 5 } - 2 } }


A) lnx+53ln(x2) \quad \ln x + \frac { 5 } { 3 } \ln ( x - 2 )
B) 23lnx+ln(2) - \frac { 2 } { 3 } \ln x + \ln ( - 2 )
C) 23lnxln(2) - \frac { 2 } { 3 } \ln x - \ln ( - 2 )
D) lnx53ln(x2) \ln x - \frac { 5 } { 3 } \ln ( x - 2 )
E) lnx13ln(x52) \quad \ln x - \frac { 1 } { 3 } \ln \left( x ^ { 5 } - 2 \right)

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