▶️ Ejercicio 298 álgebra - Solucionario Baldor ✅✅

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CAPITULO XXXVIII

Logaritmos

Ejercicio 298

Hallar el valor de las siguientes expresiones por medio de logaritmos:

$\begin{matrix} 532 \times 0.184 \\ 532 \times 0.184 & = l o g (532 \times 0.184) \\ = l o g 532 + l o g 0.184 \\ = 2.725911632 - 0.735182177 \\ = 1.99072955 \\ = a n t i l o g 1.99072955 \\ = 97.888 \end{matrix}$
$\begin{matrix} 191.7 \times 432 \\ 191.7 \times 432 & = l o g (191.7 \times 432) \\ = l o g 191.7 + l o g 432 \\ = 2.282622113 + 2.635483747 \\ = 4.91810586 \\ = a n t i l o g 4.91810586 \\ = 82814.4 \end{matrix}$
$\begin{matrix} 0.7 \times 0.013 \times 0.9 \\ 0.7 \times 0.013 \times 0.9 & = l o g (0.7 \times 0.013 \times 0.9) \\ = l o g 0.7 + l o g 0.013 + l o g 0.9 \\ = - 2.086716098 \\ = a n t i l o g - 2.086716098 \\ = 8.19 \times 1 0^{- 3} \\ = 0.00819 \end{matrix}$
$\begin{matrix} 7.5 \times 8.16 \times 0.35 \times 10037 \\ 7.5 \times 8.16 \times 0.35 \times 10037 & = l o g (7.5 \times 8.16 \times 0.35 \times 10037) \\ = l o g 7.5 + l o g 8.16 + l o g 0.35 + l o g 10037 \\ = 5.332423391 \\ = a n t i l o g 5.332423391 \\ = 214992.54 \end{matrix}$
$\begin{matrix} 3.2 \times 4.3 \times 7.8 \times 103.4 \times 0.019 \\ 3.2 \times 4.3 \times 7.8 \times 103.4 \times 0.019 & = l o g (3.2 \times 4.3 \times 7.8 \times 103.4 \times 0.019) \\ = l o g 3.2 + l o g 4.3 + l o g 7.8 + l o g 103.4 + l o g 0.019 \\ = 2.323987176 \\ = a n t i l o g 2.323987176 \\ = 210.8566 \end{matrix}$
$\begin{matrix} 95.13 \div 7.23 \\ 95.13 \div 7.23 & = l o g (95.13 \div 7.23) \\ = l o g 95.13 - l o g 7.23 \\ = 1.119179199 \\ = a n t i l o g 1.119179199 \\ = 13.15767635 \end{matrix}$
$\begin{matrix} 8.125 \div 0.9324 \\ 8.125 \div 0.9324 & = l o g (8.125 \div 0.9324) \\ = l o g 8.125 - l o g 0.9324 \\ = 0.9402211048 \\ = a n t i l o g 0.9402211048 \\ = 8.714071214 \end{matrix}$
$\begin{matrix} 7653.95 \div 12.354 \\ 7653.95 \div 12.354 & = l o g (7653.95 \div 12.354) \\ = l o g 7653.95 - l o g 12.354 \\ = 2.792078024 \\ = a n t i l o g 2.792078024 \\ = 619.5523717 \end{matrix}$
$\begin{matrix} \frac{0.72183}{0.0095} \\ \frac{0.72183}{0.0095} & = l o g (\frac{0.72183}{0.0095}) \\ = l o g 0.72183 - l o g 0.0095 \\ = 1.880711323 \\ = a n t i l o g 1.880711323 \\ = 75.98210526 \end{matrix}$
$\begin{matrix} \frac{9114}{0.02} \\ \frac{9114}{0.02} & = l o g (\frac{9114}{0.02}) \\ = l o g 9114 - l o g 0.02 \\ = 5.658679029 \\ = 455700 \end{matrix}$
$\begin{matrix} 2^{10} \\ 2^{10} & = l o g 2^{10} \\ = 10 l o g 2 \\ = 10 (0.3010299957) \\ = 3.010299957 \\ = a n t i l o g 3.010299957 \\ = 1024 \end{matrix}$
$\begin{matrix} 0.1 5^{3} \\ 0.1 5^{3} & = l o g 0.1 5^{3} \\ = 3 l o g 0.15 \\ = 3 (- 0.8239087409) \\ = - 2.471726223 \\ = a n t i l o g (- 2.471726223) \\ = 3.375 \times 1 0^{- 3} \end{matrix}$
$\begin{matrix} 18.6 5^{4} \\ 18.6 5^{4} & = l o g 18.6 5^{4} \\ = 4 l o g 18.65 \\ = 4 (1.270678836) \\ = 5.082715345 \\ = a n t i l o g (5.082715345) \\ = 120980.4915 \end{matrix}$
$\begin{matrix} 20.8 4^{2} \\ 20.8 4^{2} & = l o g 20.8 4^{2} \\ = 2 l o g 20.84 \\ = 2 (1.318897715) \\ = 2.637795429 \\ = a n t i l o g (2.637795429) \\ = 434.3056 \end{matrix}$
$\begin{matrix} 7. 2^{6} \\ 7. 2^{6} & = l o g 7. 2^{6} \\ = 6 l o g 7.2 \\ = 6 (0.8573324964) \\ = 5.143994979 \\ = a n t i l o g (5.143994979) \\ = 139314.0695 \end{matrix}$
$\begin{matrix} \sqrt{3} \\ \sqrt{3} & = l o g 3^{\frac{1}{2}} \\ = \frac{1}{2} l o g 3 \\ = \frac{1}{2} (0.4771212547) \\ = 0.2385606274 \\ = a n t i l o g (0.2385606274) \\ = 1.732050808 \end{matrix}$
$\begin{matrix} \sqrt[3]{2} \\ \sqrt[3]{2} & = l o g 2^{\frac{1}{3}} \\ = \frac{1}{3} l o g (2) \\ = \frac{1}{3} (0.3010299957) \\ = 0.1003433319 \\ = a n t i l o g (0.1003433319) \\ = 1.25992105 \end{matrix}$
$\begin{matrix} \sqrt[4]{5} \\ \sqrt[4]{5} & = l o g 5^{\frac{1}{4}} \\ = \frac{1}{4} l o g 5 \\ = \frac{1}{4} (0.6989700043) \\ = 0.1747425011 \\ = a n t i l o g (0.1747425011) \\ = 1.495348781 \end{matrix}$
$\begin{matrix} \sqrt[5]{63} \\ \sqrt[5]{63} & = l o g 6 3^{\frac{1}{5}} \\ = \frac{1}{5} l o g 63 \\ = \frac{1}{5} (1.799340549) \\ = 0.3598681099 \\ = a n t i l o g (0.3598681099) \\ = 2.290172049 \end{matrix}$
$\begin{matrix} \sqrt[7]{815} \\ \sqrt[7]{815} & = l o g 81 5^{\frac{1}{7}} \\ = \frac{1}{7} l o g 815 \\ = \frac{1}{7} (2.911157609) \\ = 0.4158796584 \\ = a n t i l o g (0.4158796584) \\ = 2.605431493 \end{matrix}$

Categories: Capítulo XXXVIII