Propiedades de Logaritmos Profesor Moisés Grillo Ing. Industrial Derechos reservados Prohibida su reproducción

𝑙𝑜𝑔 𝑥 𝑎𝑏 = 𝑙𝑜𝑔 𝑥 𝑎+ 𝑙𝑜𝑔 𝑥 𝑏 𝑙𝑜𝑔 𝑛 𝑎 𝑏 = 𝑙𝑜𝑔 𝑛 𝑎− 𝑙𝑜𝑔 𝑛 𝑏

= 𝑛 𝑚 𝑙𝑜𝑔 𝑎 𝑚 𝑎 𝑛 𝑙𝑜𝑔 𝑎 𝑎 =1 𝑙𝑜𝑔 𝑎 𝑏 𝑥 =𝑥 𝑙𝑜𝑔 𝑎 𝑏 = 1 𝑥 𝑙𝑜𝑔 𝑎 𝑏 𝑙𝑜𝑔 𝑎 𝑏 𝑥 =𝑥 𝑙𝑜𝑔 𝑎 𝑏 = 1 𝑥 𝑙𝑜𝑔 𝑎 𝑏 𝑙𝑜𝑔 𝑎 𝑥 𝑏 = 𝑛 𝑚 𝑙𝑜𝑔 𝑎 𝑚 𝑎 𝑛 𝑙𝑜𝑔 𝑎 𝑎 =1

𝑙𝑜𝑔 𝑏 𝑎 2 𝑏 𝑐 3

𝑙𝑜𝑔 𝑏 𝑎 2 𝑏 − 𝑙𝑜𝑔 𝑏 𝑐 3 𝑙𝑜𝑔 𝑏 𝑎 2 + 𝑙𝑜𝑔 𝑏 𝑏 −3 𝑙𝑜𝑔 𝑏 𝑐 𝑙𝑜𝑔 𝑏 𝑎 2 𝑏 𝑐 3 𝑙𝑜𝑔 𝑏 𝑎 2 𝑏 − 𝑙𝑜𝑔 𝑏 𝑐 3 𝑙𝑜𝑔 𝑏 𝑎 2 + 𝑙𝑜𝑔 𝑏 𝑏 −3 𝑙𝑜𝑔 𝑏 𝑐 2 𝑙𝑜𝑔 𝑏 𝑎+ 1 2 𝑙𝑜𝑔 𝑏 𝑏−3 𝑙𝑜𝑔 𝑏 𝑐 2 𝑙𝑜𝑔 𝑏 𝑎+ 1 2 −3 𝑙𝑜𝑔 𝑏 𝑐

𝑙𝑜𝑔 𝑥 𝑥 3 𝑦 − 𝑙𝑜𝑔 𝑥 𝑛 7 𝑙𝑜𝑔 𝑥 𝑥 3 + 𝑙𝑜𝑔 𝑥 𝑦 −7 𝑙𝑜𝑔 𝑥 𝑛 𝑙𝑜𝑔 𝑥 𝑥 3 𝑦 𝑛 7 𝑙𝑜𝑔 𝑥 𝑥 3 𝑦 − 𝑙𝑜𝑔 𝑥 𝑛 7 𝑙𝑜𝑔 𝑥 𝑥 3 + 𝑙𝑜𝑔 𝑥 𝑦 −7 𝑙𝑜𝑔 𝑥 𝑛 3+ 1 2 𝑙𝑜𝑔 𝑥 𝑦−7 𝑙𝑜𝑔 𝑥 𝑛

𝑙𝑜𝑔 𝑎 𝑎 5 𝑏 𝑐 2 =5+ 1 2 𝑙𝑜𝑔 𝑎 𝑏−2 𝑙𝑜𝑔 𝑎 𝑐 𝑙𝑜𝑔 𝑦 𝑥 8 5 𝑦 𝑧 5 𝑙𝑜𝑔 𝑎 𝑎 5 𝑏 𝑐 2 =5+ 1 2 𝑙𝑜𝑔 𝑎 𝑏−2 𝑙𝑜𝑔 𝑎 𝑐 𝑙𝑜𝑔 𝑦 𝑥 8 5 𝑦 𝑧 5 =8 𝑙𝑜𝑔 𝑦 𝑥+ 1 5 −5 𝑙𝑜𝑔 𝑦 𝑧 𝑙𝑜𝑔 𝑛 𝑚 2 6 𝑝 𝑛 3 =2 𝑙𝑜𝑔 𝑛 𝑚+ 1 6 𝑙𝑜𝑔 𝑛 𝑝−3 𝑙𝑜𝑔 5 𝑎 9 7 5 𝑥 8 =9 𝑙𝑜𝑔 5 𝑎+ 1 7 −8 𝑙𝑜𝑔 5 𝑥

𝑙𝑜𝑔 𝑥 𝑎 𝑏 1 2 𝑙𝑜𝑔 𝑥 𝑎 𝑏 1 2 𝑙𝑜𝑔 𝑥 𝑎+ 𝑙𝑜𝑔 𝑥 𝑏 1 2 𝑙𝑜𝑔 𝑥 𝑎+ 1 2 𝑙𝑜𝑔 𝑥 𝑏 1 2 𝑙𝑜𝑔 𝑥 𝑎+ 1 4 𝑙𝑜𝑔 𝑥 𝑏

𝑙𝑜𝑔 𝑛 3 𝑥 𝑦 1 3 𝑙𝑜𝑔 𝑛 𝑥 𝑦 1 3 𝑙𝑜𝑔 𝑛 𝑥+ 𝑙𝑜𝑔 𝑛 𝑦 1 3 𝑙𝑜𝑔 𝑛 𝑥+ 1 2 𝑙𝑜𝑔 𝑛 𝑦 1 3 𝑙𝑜𝑔 𝑛 𝑥+ 1 6 𝑙𝑜𝑔 𝑛 𝑦

= 1 5 𝑙𝑜𝑔 𝑎 𝑛 3 7 𝑏 𝑎 4 1 5 𝑙𝑜𝑔 𝑎 𝑛 3 7 𝑏 − 𝑙𝑜𝑔 𝑎 𝑎 4 𝑙𝑜𝑔 𝑎 5 𝑛 3 7 𝑏 𝑎 4 = 1 5 𝑙𝑜𝑔 𝑎 𝑛 3 7 𝑏 𝑎 4 1 5 𝑙𝑜𝑔 𝑎 𝑛 3 7 𝑏 − 𝑙𝑜𝑔 𝑎 𝑎 4 1 5 𝑙𝑜𝑔 𝑎 𝑛 3 + 𝑙𝑜𝑔 𝑎 7 𝑏 −4 1 5 3 𝑙𝑜𝑔 𝑎 𝑛+ 1 7 𝑙𝑜𝑔 𝑎 𝑏−4 3 5 𝑙𝑜𝑔 𝑎 𝑛+ 1 35 𝑙𝑜𝑔 𝑎 𝑏− 4 5

= 1 2 𝑙𝑜𝑔 𝑥 𝑥 6 3 𝑛 𝑐 8 1 2 𝑙𝑜𝑔 𝑥 𝑥 6 3 𝑛 − 𝑙𝑜𝑔 𝑥 𝑐 8 𝑙𝑜𝑔 𝑥 𝑥 6 3 𝑛 𝑐 8 = 1 2 𝑙𝑜𝑔 𝑥 𝑥 6 3 𝑛 𝑐 8 1 2 𝑙𝑜𝑔 𝑥 𝑥 6 3 𝑛 − 𝑙𝑜𝑔 𝑥 𝑐 8 1 2 𝑙𝑜𝑔 𝑥 𝑥 6 + 𝑙𝑜𝑔 𝑥 3 𝑛 −8 𝑙𝑜𝑔 𝑥 𝑐 1 2 6+ 1 3 𝑙𝑜𝑔 𝑥 𝑛−8 𝑙𝑜𝑔 𝑥 𝑐 3+ 1 6 𝑙𝑜𝑔 𝑥 𝑛−4 𝑙𝑜𝑔 𝑥 𝑐

𝑙𝑜𝑔 𝑥 3 𝑥 5 𝑛 𝑦 2 = 5 3 + 1 6 𝑙𝑜𝑔 𝑥 𝑛− 2 3 𝑙𝑜𝑔 𝑥 𝑦 𝑙𝑜𝑔 𝑎 𝑐 8 5 𝑎 𝑏 5 =4 𝑙𝑜𝑔 𝑎 𝑐+ 1 10 − 5 2 𝑙𝑜𝑔 𝑎 𝑏 𝑙𝑜𝑔 𝑦 7 𝑚 2 6 𝑛 𝑦 3 = 2 7 𝑙𝑜𝑔 𝑦 𝑚+ 1 42 𝑙𝑜𝑔 𝑦 𝑛− 3 7

=𝑙𝑜𝑔7+𝑙𝑜𝑔𝑎+3𝑙𝑜𝑔𝑏+ 1 2 𝑙𝑜𝑔5+ 1 2 𝑙𝑜𝑔 𝑐 2 𝑙𝑜𝑔 7𝑎 𝑏 3 5 𝑐 2 =𝑙𝑜𝑔 7𝑎 𝑏 3 +𝑙𝑜𝑔 5 𝑐 2 =𝑙𝑜𝑔7+𝑙𝑜𝑔𝑎+𝑙𝑜𝑔 𝑏 3 + 1 2 𝑙𝑜𝑔 5 𝑐 2 =𝑙𝑜𝑔7+𝑙𝑜𝑔𝑎+3𝑙𝑜𝑔𝑏+ 1 2 𝑙𝑜𝑔5+ 1 2 𝑙𝑜𝑔 𝑐 2 =𝑙𝑜𝑔7+𝑙𝑜𝑔𝑎+3𝑙𝑜𝑔𝑏+ 1 2 𝑙𝑜𝑔5+ 2 2 𝑙𝑜𝑔𝑐 =𝑙𝑜𝑔7+𝑙𝑜𝑔𝑎+3𝑙𝑜𝑔𝑏+ 1 2 𝑙𝑜𝑔5+𝑙𝑜𝑔𝑐

𝑙𝑜𝑔 𝑥 2∙ 2∙ 2∙ 2 𝑙𝑜𝑔 𝑥 2+ 𝑙𝑜𝑔 𝑥 2∙ 2∙ 2 𝑙𝑜𝑔 𝑥 2+ 1 2 𝑙𝑜𝑔 𝑥 2∙ 2∙ 2 𝑙𝑜𝑔 𝑥 2+ 1 2 𝑙𝑜𝑔 𝑥 2+ 𝑙𝑜𝑔 𝑥 2∙ 2 𝑙𝑜𝑔 𝑥 2+ 1 2 𝑙𝑜𝑔 𝑥 2+ 1 2 𝑙𝑜𝑔 𝑥 2∙ 2

𝑙𝑜𝑔 𝑥 2+ 1 2 𝑙𝑜𝑔 𝑥 2+ 1 4 𝑙𝑜𝑔 𝑥 2∙ 2 𝑙𝑜𝑔 𝑥 2+ 1 2 𝑙𝑜𝑔 𝑥 2+ 1 4 𝑙𝑜𝑔 𝑥 2+ 𝑙𝑜𝑔 𝑥 2 𝑙𝑜𝑔 𝑥 2+ 1 2 𝑙𝑜𝑔 𝑥 2+ 1 4 𝑙𝑜𝑔 𝑥 2+ 1 2 𝑙𝑜𝑔 𝑥 2 1 𝑙𝑜𝑔 𝑥 2+ 1 2 𝑙𝑜𝑔 𝑥 2+ 1 4 𝑙𝑜𝑔 𝑥 2+ 1 8 𝑙𝑜𝑔 𝑥 2 1+ 1 2 + 1 4 + 1 8 𝑙𝑜𝑔 𝑥 2 8+4+2+1 8 𝑙𝑜𝑔 𝑥 2 = 15 8 𝑙𝑜𝑔 𝑥 2