Write the expression using only the indicated logarithms.
-$\log _ { 3 } ( x + y )$ using natural logarithms
A) $\ln ( x + y ) + \ln 3$
B) $\frac { \ln 3 } { \ln ( x + y ) }$
C) $\ln ( x + y ) \ln 3$
D) $\frac { \ln ( x + y ) } { \ln 3 }$

Question

Quizplus · Accepted Answer

The correct expression is obtained by using the change of base formula for logarithms, which is $\log_b a = \frac{\ln a}{\ln b}$. Applying this formula, $\log_3(x+y)$ becomes $\frac{\ln(x+y)}{\ln 3}$.

Write the Expression Using Only the Indicated Logarithms log⁡3(x+y)\log _ { 3 } ( x + y )log3​(x+y)

Write the Expression Using Only the Indicated Logarithms $\log _ { 3 } ( x + y )$