Rewrite the expression as a sum, difference, or multiple of logarithms.
-$\ln \frac { \sqrt [ 3 ] { 2 x + 10 } } { 7 x ^ { 2 } }$
A) $\frac { 1 } { 3 } \ln 2 x + \ln 10 - 2 \ln 7 x$
B) $3 \ln ( 2 x + 10 ) - 2 \ln 7 x$
C) $\frac { 1 } { 3 } \ln ( 2 x + 10 ) - \ln 7 + 2 \ln x$
D) $\frac { 1 } { 3 } \ln ( 2 x + 10 ) - \ln 7 - 2 \ln x$

Question

Quizplus · Accepted Answer

The expression can be rewritten using the properties of logarithms: the quotient rule $\ln(a/b) = \ln(a) - \ln(b)$, the power rule $\ln(a^b) = b\ln(a)$, and the root rule $\ln(\sqrt[b]{a}) = \frac{1}{b}\ln(a)$. Applying these rules, we get $\frac{1}{3}\ln(2x+10) - \ln(7) - 2\ln(x)$.

Rewrite the Expression as a Sum, Difference, or Multiple of Logarithms