Logaritmos

PROBLEMAS PROPUESTOS
Realizar los siguientes cálculos mediante logaritmos naturales y de base 10:
a) y = 2345*3487 R: 8.177.015,00
ln⁡y=ln⁡(2345×3487)
ln⁡y=ln⁡2345+ln⁡3487
ln⁡y=7,760040681+8,156797047
ln⁡y=15,91683773
y=e^x 15,91683773
y=8.177.015,00

log⁡y=log⁡(2345×3487)
log⁡y=log⁡2345+log⁡3487log⁡y=3,370142847+3,542451947
log⁡y=6,912594794
y=〖10〗^x 6,912594794
y=8.177.015,00

b) y = 1256*3454,23 R: 4.338.512,88
ln⁡y=ln⁡(1256×3454,23)
ln⁡y=ln⁡1256+ln⁡3454,23
ln⁡y=7,135687347+8,147354846
ln⁡y=15,28304219
y=e^x 15,28304219
y=4.338.512,88

log⁡y=log⁡(1256×3454,23)
log⁡y=log⁡1256+log⁡3454,23
log⁡y=3,098989639+3,538351252log⁡y=6,637340891
y=〖10〗^x 6,637340891
y=4.338.512,88

c) y = 5463/345 R: 15,83
ln⁡y=ln⁡(5463÷345 )
ln⁡y=ln⁡5463-ln⁡345
ln⁡y=8,605753368-5,843544417
ln⁡y=2,762208951
y=e^x 2,762208951
y= 15,83

log⁡y=log⁡(5463÷345 )
log⁡y=log⁡5463-log⁡345
log⁡y=3,737431201-2,537819095
log⁡y=1,199612106
y=〖10〗^x1,199612106
y= 15,83

Realizar los siguientes cálculos mediante logaritmos naturales y de base 10:
a) y = (15,45)7 R: 210.135.479,98
ln⁡y=ln⁡〖〖15,45〗^7 〗
ln⁡y=7 ln⁡15,45
ln⁡y=7(2,737609003)
ln⁡y=19,16326302
y=e^x 19,16326302
y=210.135.479,98

log⁡y=log⁡〖〖15,45〗^7 〗
log⁡y=7 log⁡15,45
log⁡y=7(1,188928484)log⁡y=8,322499386
y=〖10〗^x 8,322499386
y=210.135.479,98
b) y = (51,1)5,2 R: 765.224.173,02
ln⁡y=ln⁡〖〖51,1〗^5,2 〗
ln⁡y=5,2 ln⁡51,1
ln⁡y=5,2(3,933784497)
ln⁡y=20,45567939
y=e^x 20,45567939
y=765.224.173,02

log⁡y=log⁡〖〖51,1〗^5,2 〗
log⁡y=5,2 log⁡51,1
log⁡y=5,2(1,7084209)
log⁡y=8,883788681
y=〖10〗^x 8,883788681y=765.224.173,02

c) y =√(3&456) R: 7,697
y=〖(456)〗^(1⁄3)
ln⁡y=ln⁡〖(456)^(1⁄3) 〗
ln⁡y=1/3 ln⁡456
ln⁡y=1/3 (6,12249281)
ln⁡y=2,040830937
y=e^x 2,040830937
y=7,697

y=〖(456)〗^(1⁄3)
log⁡y=log⁡〖(456)^(1⁄3) 〗
log⁡y=1/3 log⁡456
log⁡y=1/3 (2,658964843)
log⁡y=0,886321614
y=〖10〗^x 0,886321614
y=7,697

Realizar los siguientescálculos mediante logaritmos naturales y de base 10:
a) y = 453*213/670 R: 144,01
ln⁡y=ln⁡(453×213÷670)
ln⁡y=ln⁡453+ln⁡213-ln⁡670
ln⁡y=6,115892125+5,361292166-6,507277712
ln⁡y=4,969906579
y=e^x 4,969906579
y=144,01

log⁡y=log⁡(453×213÷670)
log⁡y=log⁡453+log⁡213-log⁡670
log⁡y=2,656098202+2,328379603-2,826074803log⁡y=2,158403002
y=〖10〗^x 2,158403002
y=144,01

b) y = (2300/3454)*(1200/45) R: 17,76
ln⁡y=ln⁡[(2300÷3454)×(1200÷45)]
ln⁡y=(ln⁡2300-ln⁡3454 )+(ln⁡1200-ln⁡45 )
ln⁡y=(7,740664402-8,147288259)+(7,090076836-3,80666249)
ln⁡y=-0,406623857+3,283414346
ln⁡y=2,876790489
y=e^x 2,876790489
y=17,76

log⁡y=log⁡[(2300÷3454)×(1200÷45)]log⁡y=(log⁡2300-log⁡3454 )+(log⁡1200-log⁡45 )
log⁡y=(3,361727836-3,538322333)+(3,079181246-1,653212514)
log⁡y=-0,176594497+1,425968732
log⁡y=1,249374235
y=〖10〗^x 1,249374235
y=17,76

c) y = 0,1231/(231*0,112) R: 0,004758
ln⁡y=ln⁡[0,1231÷(231×0,112)]
ln⁡y=ln⁡0,1231-(ln⁡231+ln⁡0,112 )
ln⁡y=-2,094758246-(5,442417711-2,189256408)ln⁡y=-2,094758246-3,253161303
ln⁡y=-5,347919549
y=e^x-5,347919549
y=0,004758

log⁡y=log⁡[0,1231÷(231×0,112)]
log⁡y=log⁡0,1231-(log⁡231+log⁡0,112 )
log⁡y=-0,909741947-(2,36361198-0,950781977)
log⁡y=-0,909741947-1,412830003
log⁡y=-2,32257195
y=〖10〗^x-2,32257195
y=0,004758

Realizar los siguientes cálculos mediante logaritmos naturales y de base 10:
a) y = (23,4*45,4)*(1,545)7...