UFSC - Determine a parte inteira do valor do logaritmo

[lew_ax]

(UFSC) Se \(x=\sqrt[3]{360}\), \(log_{10}2=0,301\) e \(log_{10}3=0,477\), determine a PARTE INTEIRA do valor de \(20.log_{10}x\).

R=17

[Sobolev]

\(20 \log_{10} 360^{1/3} = \frac{20}{3}(\log_{10} (2^3 \times 3^2 \times 5)) = \frac{20}{3}(3 \log_{10} 2 + 2 \log_{10}3 +\log_{10} (10/2))=
\frac{20}{3}( 3 \times 0.301 + 2 \times 0.477 + 1 - 0.301) = \frac{20}{3} \times 2.558 = 17.05333\)