Question

expand each expression.
$ln (2x)^4$

• $4 ln 2 + 4 ln x$
• $4 ln 2 + ln x$ (marked with a red cross)
• $8 ln x$

retry

Explanation:

Step1: Apply Log Power Rule

The power rule of logarithms states that \(\ln(a^b) = b\ln(a)\). So for \(\ln((2x)^4)\), we can bring the exponent 4 down: \(\ln((2x)^4)=4\ln(2x)\).

Step2: Apply Log Product Rule

The product rule of logarithms states that \(\ln(ab)=\ln(a)+\ln(b)\). Applying this to \(\ln(2x)\), we get \(\ln(2x)=\ln(2)+\ln(x)\).

Step3: Substitute and Simplify

Substitute \(\ln(2x)=\ln(2)+\ln(x)\) into \(4\ln(2x)\): \(4(\ln(2)+\ln(x)) = 4\ln(2)+4\ln(x)\).

Answer:

A. \(4\ln 2 + 4\ln x\)