Respuestas sección 4.1

Ejercicios 1 al 10. Método de evaluación para obtener los ceros de los siguientes polinomios.

  1. $\hspace{0.1cm}\left(x+1\right)\left(x-2\right)\left(x-3\right)\left(x^2+3x+4\right)\\[0.2cm]$
  2. $\hspace{0.1cm}\left(x+2\right)\left(x-3\right)\left(x+4\right)\left(3x+2\right)\left(2x-1\right)\\[0.2cm]$
  3. $\hspace{0.1cm}\left(x-2\right)\left(x-3\right)\left(x+3\right)\\[0.2cm]$
  4. $\hspace{0.1cm}\left(x+1\right)^2\left(x+2\right)\left(x-4\right)\\[0.2cm]$
  5. $\hspace{0.1cm}\left(a+5\right)\left(a-4\right)\left(a+1\right)\left(a-2\right)\left(a-3\right)\left(a+3\right)\\[0.2cm]$
  1. $\hspace{0.1cm}\left(a^3-2\right)\left(a-2\right)\left(a+2\right)\left(a-4\right)\left(a+4\right)\\[0.2cm]$
  2. $\hspace{0.1cm}\left(x-2\right)^2\left(x+1\right)\left(x-1\right)\\[0.2cm]$
  3. $\hspace{0.1cm}\left(x-4\right)\left(x+3\right)\left(x-2\right)\left(x+1\right)\\[0.2cm]$
  4. $\hspace{0.1cm}\left(n-5\right)\left(n+4\right)\left(n-2\right)\left(n+3\right)\\[0.2cm]$
  5. $\hspace{0.1cm}\left(3x+5\right)\left(5x-2\right)\left(x-1\right)\left(x+6\right)\\[0.2cm]$

Respuesta a los ejercicios 11 y 20. Ecuaciones exponenciales.

  1. $\hspace{0.1cm}x=\frac{log\;\left(\frac{2}{81}\right)}{log\;\left(24\right)}\approx -1.16\\[0.2cm]$
  2. $\hspace{0.1cm}x=-\frac{log\;\left(200\right)}{log\;\left(\frac{4}{5}\right)}\approx 23.744\\[0.2cm]$
  3. $\hspace{0.1cm}x=-\frac{log\;\left(1600\right)}{log\;\left(\frac{16}{5}\right)}\approx -6.343\\[0.2cm]$
  4. $\hspace{0.1cm}x=-\frac{log\;\left(5308416\right)}{log\;\left(\frac{3}{2}\right)}\approx -38.19\\[0.2cm]$
  5. $\hspace{0.1cm}x=-2\\[0.2cm]$
  1. $\hspace{0.1cm}x=3\\[0.2cm]$
  2. $\hspace{0.1cm}x=\frac{11}{4}\\[0.2cm]$
  3. $\hspace{0.1cm}x=-3\\[0.2cm]$
  4. $\hspace{0.1cm}x=2\\[0.2cm]$
  5. $\hspace{0.1cm}x=-4\\[0.2cm]$

Ejercicios 21 y 30. Ecuaciones logaritmicas.

  1. $\hspace{0.1cm}x=7\\[0.2cm]$
  2. $\hspace{0.1cm}x=2\\[0.2cm]$
  3. $\hspace{0.1cm}x=\frac{7}{2}\\[0.2cm]$
  4. $\hspace{0.1cm}x=\pm 8\\[0.2cm]$
  5. $\hspace{0.1cm}x=\frac{3}{2}\\[0.2cm]$
  1. $\hspace{0.1cm}x=20\wedge y=2\\[0.2cm]$
  2. $\hspace{0.1cm}x=10\wedge y=1\\[0.2cm]$
  3. $\hspace{0.1cm}x=100\wedge y=10\\[0.2cm]$
  4. $\hspace{0.1cm}x=100\wedge y=10^{-1}\\[0.2cm]$
  5. $\hspace{0.1cm}x=100\wedge y=10\\[0.2cm]$

Ejercicios 31 y 40. Problemas de aplicación.

  1. $\hspace{0.1cm}3 \wedge \cfrac{1}{3}$
  2. $\hspace{0.1cm}10\wedge 15$
  3. $\hspace{0.1cm}85 $
  4. $\hspace{0.1cm}30m. \times 60m.$
  5. $\hspace{0.1cm}$45 años y 9 años
  1. $\hspace{0.1cm}\left(3\sqrt{73}-21\right)\;$metros
  2. $\hspace{0.1cm}\cfrac{15}{2}\wedge \cfrac{3}{2} $
  3. $\hspace{0.1cm}$1.3 cm.
  4. $\hspace{0.1cm}$50 galones del primer tanque y 40galones del segundo tanque.
  5. $\hspace{0.1cm}$A=4,B=2,C=5 Horas respectivamente