Question

expand: ln (4a)³
○ 3 ln 4 + ln a
○ 3 ln 4 - 3 ln a
○ 3 ln 4 + 3 ln a

Explanation:

Step1: Apply Log Power Rule

The power rule of logarithms states that $\ln(x^n) = n\ln(x)$. For $\ln((4a)^3)$, we can apply this rule first. So, $\ln((4a)^3)=3\ln(4a)$.

Step2: Apply Log Product Rule

The product rule of logarithms states that $\ln(xy)=\ln(x)+\ln(y)$. Now, apply this to $\ln(4a)$, where $x = 4$ and $y=a$. So, $\ln(4a)=\ln(4)+\ln(a)$.

Step3: Substitute and Simplify

Substitute $\ln(4a)=\ln(4)+\ln(a)$ back into $3\ln(4a)$. We get $3(\ln(4)+\ln(a)) = 3\ln(4)+3\ln(a)$.

Answer:

$3\ln 4 + 3\ln a$ (corresponding to the option "3 ln 4 + 3 ln a")