Start with the given equation:

\(\ln(x^3 - 3) = 3 \ln x - \ln 3\)

Apply the logarithm property \(a \ln b = \ln(b^a)\):

\(\ln(x^3 - 3) = \ln(x^3) - \ln 3\)

Use the property \(\ln a - \ln b = \ln\left(\frac{a}{b}\right)\):

\(\ln(x^3 - 3) = \ln\left(\frac{x^3}{3}\right)\)

Since the logarithms are equal, set the arguments equal:

\(x^3 - 3 = \frac{x^3}{3}\)

Multiply through by 3 to clear the fraction:

\(3(x^3 - 3) = x^3\)

\(3x^3 - 9 = x^3\)

Rearrange to solve for \(x^3\):

\(3x^3 - x^3 = 9\)

\(2x^3 = 9\)

Divide by 2:

\(x^3 = \frac{9}{2}\)

Take the cube root:

\(x = \sqrt[3]{\frac{9}{2}}\)

Calculate \(x\) to 3 significant figures:

\(x \approx 1.65\)