1.5 PROBLEMAS PROPUESTOS
1. Realizar los siguientes cálculos mediante logaritmos naturales y de base 10:
a.
y=2345∗3487
R=
8.177 .015
Logaritmo natural Base 10
ln y=ln 2345+ln 3487
≈7.760040681+8.156797047
≈15.91683773
log y=log 2345+log 3487
≈3.370142847+3.542451947
≈6,912594794
Antilogaritmo
e
15.91683773
=8177015
10
6,912594794
=8177015
b.
y=1256∗3454.23
R=
4338512.88
Logaritmo natural Base 10
ln y=ln 1256+ln 3454.23
≈7.1 35687347+8.1 4 7354846
≈15.2 8304219
log y=log 1256 +log 3454.23
≈3.09 8989639+3.5 38351252
≈6.6 37340891
Antilogaritmo
e
15.2830 4219
=4338512.88
10
6.637340891
=4338512.88
c.
y=5463
345
R=
15.83478261
Logaritmo natural Base 10
ln y=ln 5463−ln345
≈8.6 05753368−5.84 354441 7
≈2. 762208951
log y=log5463−log 345
≈3.7 37431201−2.5 37819095
≈1. 199612105
Antilogaritmo
e
2.762208951
=15.83478261
10
1.199612105
=15.83478261
2. Realizar los siguientes cálculos mediante logaritmos naturales y de base 10:
a.
y=15.457
R=
210135479,98
Logaritmo natural Base 10
ln y=7 ln 15.45
≈7
(
2.737609003
)
≈19.16326302
log y=7 log15.45
≈7
(
1.188928484
)
≈8.322499386
Antilogaritmo
e
19.16326302
≈210135480
10
8.322499386
=210135480
b.
y=51.15.2
R=
765224173,02
Logaritmo natural Base 10
ln y=5.2∗ln 51.1
≈5.2
(
3.933784497
)
≈20.45567939
log y=5.2∗log 51.1
≈5.2
(
1.7084209
)
≈8.883788681
Antilogaritmo
e
20.45567939
≈765224173
10
8.883788681
=765224173
c.
y=
3
√
456
R=
7,697
