By Murray Spiegel, Larry Stephens
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El −1/2 se descarta como solución, ya que los logaritmos de números negativos no están definidos. y = 5/3 demuestra ser una solución cuando se sustituye en la ecuación original. Por lo tanto, la única solución es y = 5/3. EJEMPLO 39 Resuelva la ecuación logarítmica siguiente: ln(5x) − ln(4x + 2) = 4 La diferencia de logaritmos se convierte en el logaritmo del cociente, ln(5x/(4x + 2)) = 4. 59815. 5117. Sin embargo, esta respuesta no satisface la ecuación ln(5x) − ln(4x + 2) = 4, ya que la función log no está definida para números negativos.
0125)ˆ(4*B1), se hace clic y se arrastra desde B2 hasta F2. 05*B1), se hace clic y se arrastra desde B3 hasta F3. El interés continuo compuesto da resultados ligeramente mejores. PROPIEDADES DE LOS LOGARITMOS Las propiedades más importantes de los logaritmos son las siguientes: 1. logb MN = logb M + logb N 2. logb M/N = logb M − logb N 3. logb M P = p logb M EJEMPLO 36 Escriba logb(xy4/z3) como suma o diferencia de logaritmos de x, y y z. xy 4 = log b xy 4 log b z 3 propiedad 2 z3 xy 4 log b 3 = log b x + log b y 4 log b z 3 propiedad 1 z xy 4 log b 3 = log b x + 4 log b y 3 log b z propiedad 3 z log b ECUACIONES LOGARÍTMICAS Para resolver ecuaciones logarítmicas: 1.
8 televisores por hogar. 8 elabore una gráfica de pastel usando EXCEL. 8. 8. 29 Resuelva las siguientes ecuaciones: 20 = 8 a) 4a b) 3X + 4 = 24 2X c) 18 5b = 3(b + 8) + 10 Y +2 Y d) +1= 3 2 SOLUCIÓN a) b) Sumar 20 a ambos miembros: 4a − 20 + 20 = 8 + 20 o bien 4a = 28. Dividir ambos lados entre 4: 4a/4 = 28/4 y a = 7. Verificación: 4(7) − 20 = 8, 28 − 20 = 8 y 8 = 8. Restar 4 de ambos miembros: 3X + 4 − 4 = 24 − 2X − 4 o bien 3X = 20 − 2X. Sumar 2X a ambos lados: 3X + 2X = 20 − 2X + 2X o bien 5X = 20.