Write down the first three terms of the Maclaurin series for \(\ln \left( 1 + x ^ { 3 } \right)\).
Use these three terms to show that \(\ln ( 1.125 ) \approx \frac { n } { 1536 }\), where \(n\) is an integer to be determined.
Charlie uses the same first three terms of the series to approximate \(\ln 9\) and gets an answer of 147, correct to 3 significant figures. However, \(\ln 9 = 2.20\) correct to 3 significant figures. Explain Charlie's error.