Ecuaciones con Logaritmos Profesor Moisés Grillo Ing. Industrial Derechos reservados Prohibida su reproducción
𝑙𝑜𝑔 2 𝑥+1 =3
𝑙𝑜𝑔 2 𝑥+1 =3 𝑥+1=8 𝑥=8−1 𝑥=7
𝑵ú𝒎𝒆𝒓𝒐 𝒅𝒆 𝒍𝒐𝒈𝒂𝒓𝒊𝒕𝒎𝒐 𝒍𝒐𝒈𝒂𝒓𝒊𝒕𝒎𝒐 𝑙𝑜𝑔 2 8=3 8 = 2 3 𝑩𝒂𝒔𝒆 𝒅𝒆 𝒍𝒐𝒈𝒂𝒓𝒊𝒕𝒎𝒐
𝑙𝑜𝑔 2 𝑥=4 𝑥= 2 4 =16 𝑙𝑜𝑔 5 𝑦=3 𝑦= 5 3 =125 𝑙𝑜𝑔 4 𝑎=3 𝑎= 4 3 =64 𝑙𝑜𝑔 17 𝑏=0 𝑏= 17 0 =1
𝑙𝑜𝑔 3 𝑥+4 =2 𝑥+4=9 𝑥=9−4 𝑥=5
𝑙𝑜𝑔 7 𝑥−3 =1 𝑥−3=7 𝑥=7+3 𝑥=10
𝑙𝑜𝑔 6 𝑥−8 =0 𝑥−8=1 𝑥=1+8 𝑥=9
𝑙𝑜𝑔 𝑥+2 =2 𝑥+2=100 𝑥=100−2 𝑥=98
𝑙𝑜𝑔 7 𝑥+1 =1 𝑥=6 𝑙𝑜𝑔 6 𝑥−4 =2 𝑥=40 𝑙𝑜𝑔 3 𝑥+7 =3 𝑥=20 𝑙𝑜𝑔 2 𝑥−2 =4 𝑥=18 𝑙𝑜𝑔 𝑥+5 =1 𝑥=5
𝑙𝑜𝑔 5 3𝑥+1 =2 3𝑥+1=25 3𝑥=25−1 𝑥= 24 3 𝑥=8
𝑙𝑜𝑔 17 4𝑥−7 =0 4𝑥−7=1 4𝑥=1+7 𝑥= 8 4 𝑥=2
𝑙𝑜𝑔 6 12−4𝑥 =2 12−4𝑥= 6 2 −4𝑥=36−12 𝑥= 24 −4 𝑥=−6
𝑙𝑜𝑔 2 3𝑥+4 =4 𝑥=4 𝑙𝑜𝑔 3 5−2𝑥 =3 𝑥=−11 𝑙𝑜𝑔 4 6+5𝑥 =2 𝑥=2 𝑙𝑜𝑔 5 −1−3𝑥 =1 𝑥=−2 𝑙𝑜𝑔 2𝑥+7 =0 𝑥=−3
𝑙𝑜𝑔 3 𝑥+1 =−1 𝑥+1= 3 −1 𝑥= 1 3 −1 𝑥= 1−3 3 𝑥=− 2 3
𝑙𝑜𝑔 2 3−4𝑥 =−3 3−4𝑥= 2 −3 3−4𝑥= 1 2 3 −4𝑥= −23 8 𝑥= −23 −32 𝑥= 23 32 𝑙𝑜𝑔 2 3−4𝑥 =−3 −4𝑥= −23 8 3−4𝑥= 2 −3 𝑥= −23 −32 3−4𝑥= 1 2 3 𝑥= 23 32 −4𝑥= 1 8 −3 −4𝑥= 1−24 8
𝑙𝑜𝑔 5 𝑥+5 =−1 𝑙𝑜𝑔 7 3−𝑥 =−1 𝑙𝑜𝑔 3 2𝑥−3 =−2 𝑙𝑜𝑔 2 5−7𝑥 =−3 𝑥=− 24 5 𝑙𝑜𝑔 5 𝑥+5 =−1 𝑥= 20 7 𝑙𝑜𝑔 7 3−𝑥 =−1 𝑥= 14 9 𝑙𝑜𝑔 3 2𝑥−3 =−2 𝑥= 39 56 𝑙𝑜𝑔 2 5−7𝑥 =−3
𝑙𝑜𝑔 2 𝑥 3 +9 =4 𝑥 3 +9=16 𝑥 3 =16−9 𝑥 3 =7 𝑥=21
𝑙𝑜𝑔 5 𝑥 7 −4 =2 𝑥 7 −4= 5 2 𝑥 7 =5+4 𝑥 7 =9 𝑥=63
𝑙𝑜𝑔 3 7 2𝑥 5 +9 =3 2𝑥 5 +9= 3 7 3 2𝑥=−10 𝑥= −10 2 2𝑥 5 =7−9 𝑥=−5 2𝑥 5 =−2
𝑙𝑜𝑔 5 6 + 3𝑥 4 =3 5 6 + 3𝑥 4 = 1000 1 𝑚𝑐𝑚=12 5 6 + 3𝑥 4 = 10 3 10+9𝑥=12000 6−4 2 9𝑥=12000−10 3 2 2 𝑥= 11990 9 3 1 3 1 12
𝑥=9 𝑥=−4 𝑥=25 𝑥=− 45 14 𝑙𝑜𝑔 2 𝑥 3 +5 =3 𝑙𝑜𝑔 5 3− 𝑥 2 =2 𝑙𝑜𝑔 2 𝑥 3 +5 =3 𝑥=9 𝑙𝑜𝑔 5 3− 𝑥 2 =2 𝑥=−4 𝑙𝑜𝑔 5 7 2𝑥 5 −3 =5 𝑥=25 𝑥=− 45 14 𝑙𝑜𝑔 5 2 − 7𝑥 3 =1