Use the properties of logarithms to write the expression $\ln \left( x \sqrt [ 5 ] { x ^ { 2 } + 8 } \right)$ as a sum, difference, or multiple of logarithms.
A) $\ln x + \frac { 1 } { 8 } \ln \left( x ^ { 2 } + 5 \right)$
B) $\ln \left( x ^ { 2 } + 8 \right) + \frac { 1 } { 5 } \ln x$
C) $\ln x + \frac { 1 } { 5 } \ln \left( x ^ { 2 } + 8 \right)$
D) $\ln \left( x ^ { 2 } + 5 \right) + \frac { 1 } { 8 } \ln x$
E) $\ln x + \ln \left( x ^ { 2 } + 8 \right)$

Question

Quizplus · Accepted Answer

The expression can be rewritten using the properties of logarithms: $\ln \left( x \sqrt [ 5 ] { x ^ { 2 } + 8 } \right)$ can be split into the sum of two logarithms because $\ln(ab) = \ln(a) + \ln(b)$. The square root of $x^2 + 8$ to the fifth root can be expressed as raising $x^2 + 8$ to the power of $\frac{1}{5}$, so the expression becomes $\ln(x) + \frac{1}{5}\ln(x^2 + 8)$.

Use the Properties of Logarithms to Write the Expression ln⁡(xx2+85)\ln \left( x \sqrt [ 5 ] { x ^ { 2 } + 8 } \right)ln(x5x2+8​)

Use the Properties of Logarithms to Write the Expression $\ln \left( x \sqrt [ 5 ] { x ^ { 2 } + 8 } \right)$