Question

Use the properties of logarithms, given that ln(2) ≈ 0.6931 and ln(3) ≈ 1.0986, to approximate the logarithm. Use a calculator to confirm your approximations. (Round your answers to four decimal places.) I JUST NEED C!

Answer 1

Let's simplify the logarithm to use the value given:

$\begin{gathered} \ln(\sqrt[3]{18})=\ln(18^{\frac{1}{3}}) \\ =\frac{1}{3}\ln18 \\ =\frac{1}{3}\ln(9*2) \\ =\frac{1}{3}\lbrack\ln9+\ln2\rbrack \\ =\frac{1}{3}\lbrack\ln3^2+\ln2\rbrack \\ =\frac{1}{3}\lbrack2\ln3+\ln2\rbrack \\ =\frac{1}{3}\lbrack(2)(1.0986)+(0.6931)\rbrack \\ =0.9634 \end{gathered}$

Therefore:

$\ln(\sqrt[3]{18})=0.9634$