Expand the given logarithmic expression. Assume all variable expressions represent positive real numbers. $\ln \left( x ^ { 7 / 4 } y ^ { 3 / 2 } \right)$
A) $\frac { 21 } { 8 } \ln x y$
B) $\frac { 21 } { 8 } \ln x \ln y$
C) $x \ln \left( \frac { 7 } { 4 } \right) + y \ln \left( \frac { 3 } { 2 } \right)$
D) $\frac { 3 } { 2 } \ln x + \frac { 7 } { 4 } \ln y$
E) $\frac { 7 } { 4 } \ln x + \frac { 3 } { 2 } \ln y$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, specifically the power rule ($\ln(a^b) = b \ln(a)$) and the product rule ($\ln(ab) = \ln(a) + \ln(b)$), the expression $\ln(x^{7/4}y^{3/2})$ can be expanded to $\frac{7}{4}\ln(x) + \frac{3}{2}\ln(y)$.

Expand the Given Logarithmic Expression ln⁡(x7/4y3/2)\ln \left( x ^ { 7 / 4 } y ^ { 3 / 2 } \right)ln(x7/4y3/2)

Expand the Given Logarithmic Expression $\ln \left( x ^ { 7 / 4 } y ^ { 3 / 2 } \right)$