Question

solve: 2 ln 3 = ln(x - 4)
x = 9
x = 10
x = 13
done

Explanation:

Step1: Use logarithm power rule

Recall that \(a\ln b=\ln(b^a)\). So, \(2\ln 3=\ln(3^2)=\ln 9\). The equation becomes \(\ln 9=\ln(x - 4)\).

Step2: Use one - to - one property of logarithms

If \(\ln a=\ln b\), then \(a = b\) (for \(a>0,b>0\)). So, from \(\ln 9=\ln(x - 4)\), we get \(9=x - 4\).

Step3: Solve for x

Add 4 to both sides of the equation \(9=x - 4\). We have \(x=9 + 4=13\).

Answer:

\(x = 13\)