Question

solve: 3 ln x = ln 216
x=3
x=6
x=72
done

Explanation:

Step1: Use logarithm power rule

Recall the logarithm power rule: \( n\ln a=\ln(a^n) \). Apply it to the left - hand side of the equation \( 3\ln x=\ln 216 \), we get \( \ln(x^3)=\ln 216 \).

Step2: Use one - to - one property of logarithms

If \( \ln a=\ln b \), then \( a = b \) (since the natural logarithm function \( y = \ln x \) is one - to - one). So from \( \ln(x^3)=\ln 216 \), we can conclude that \( x^3=216 \).

Step3: Solve for x

We need to find the value of \( x \) such that \( x^3 = 216 \). We know that \( 6\times6\times6=6^3 = 216 \), so \( x = 6 \).

Answer:

B. \( x = 6 \) (assuming the options are labeled as A. \( x = 3 \), B. \( x = 6 \), C. \( x = 72 \))