EJERCICIO 301
1. 1. 1. 1. 1. ( )
5 3
5 3
5 3
0 69897 0 477121
0 477121
0 69897
0 6826
x
xLog
x
x
x
=
=
=
=
=
=
log
log log
, ,
,
,
,
,
2. 2. 2. 2. 2. 7 512
7 512
7 512
2 70927
0 845098
3 205864
3 2059
x
xLog
x
x
x
≅
log
log log
,
,
,
,
3. 3. 3. 3. 3. ( )
0 2 0 0016
0 2 0 0016
0 2 0 0016
1 30103 3 20412
3 20412
1 30103
3
0 69897
0 20412
0 69897
4 29203 0 29203
4
, ,
, log ,
log , log ,
, ,
,
,
5. 5. 5. 5. 5. ( )
( )( )
3 729
3 729
1 3 729
1 0 477121 2 86273
1 6 00944
6 00944 1
5 00944 5
1
1
x
xLog
x
x
x
=
=
+ =
+ =
+ =
= −
= ⇒ ≅
log log
, ,
,
,
6. 6. 6. 6. 6. ( )
5 625
5 625
2 5 2 79588
2
2 79588
0 69897
2 4 6
2
2
x
xLog
x
x
x x
−
−
=
=
− =
− =
− = ⇒ =
log
log ,
,
,
7. 7. 7. 7. 7. ( )
( )( )
2 128
2 128
3 1 2 2 10721
3 1 0 30103 2 10721
3 1 7
3 6
2
3 1
3 1
x
xLog
x
x
x
x
x
+
+
=
=
+ =
+ =
+ =
=
=
log
log ,
, ,
8. 8. 8. 8. 8. ( )
( )( )
3 2 187
3 2 187
2 1 3 3 33985
2 1 0 477121 3 33985
2 1 7
2 8 4
2 1
2 1
x
xLog
x
x
x x
−
−
=
=
− =
− =
− = ⇒ =
.
log .
log ,
, ,
9. 9. 9. 9. 9. 11 915
11 915
2 11 2 96142
2
2 96142
1 04139
2 2 84372
1 42186
2
2
x
xLog
x
x
x
x
=
=
=
=
=
=
log
log ,
,
,
,
,

EJERCICIO 302
1. 1. 1. 1. 1. a u r
n
Log Co
Log
n
n
= = = ÷ =
= +
+
= +
+
= + = + =
3 48 6 3 2
48 3
2
1
1 68124 1 522879
0 30103
1
1 204119
0 30103
1 4 1 5
log
, ,
,
,
2. 2. 2. 2. 2. a u r
n
Log Co
Log
n
Log co co
Log
n
n n n
= = =
= + + +
= + + +
= + = + = ≅
2
243
16
3
2
2
3
2
1
243 16 2
1 5
1
2 38461 2 79588 1 69897
0 176091
1
0 87946
0 176091
1 4 994 1 5 994 6
243
16 log
log log
,
, , ,
,
,
3. 3. 3. 3. 3. a u r
n
Log Co
Log
n
n
= = = ÷ =
= + +
= + +
= + = + =
4 512 8 4 2
512 4
2
1
2 70927 1 39794
0 30103
1
2 10721
0 30103
1 7 1 8
log
, ,
,
,
4. 4. 4. 4. 4. a u r
n
Log Co
Log
n
Log Co Co
Log Co
n
n
n
n
= = = =
= +
= + +
= + +
= + +
= +
= +
=
≅
6
2 048
81
8
6
4
3
2 048
81
6
4
3
2 048 81 6
4 3
3 31133 2 09151 1 22184
0 60206 1 522879
1
0 62468
0 124939
1
4 999879 1
5 999879
6
.
.
log
. log log
log
, ,
, ,
5. 5. 5. 5. 5. a u r
n
Log Co
Log
n
Log Co Co
Log
n
n
= = = =
= +
+
= +
+
= +
+
= + = + =
2
625
8
5
2
2 5
625
8
2
2 5
1
625 8 2
2 5
1
2 79588 1 09691 1 69897
0 39794
1
1 59176
0 39794
1 4 1 5
,
log
,
log log
,
, ,
,
,

EJERCICIO 303
1. 1. 1. 1. 1. ( )
( )
( )
( )
c r t
C
C
Log C Log
Log C Log
Log C
Log C
Anti
= = =
= +
=
=
= +
= +
=
=
500 0 06 3
500 1 0 06
500 1 06
500 1 06
500 3 1 06
2 69897 3 0 02531
2 7749
2 7749 595 51
3
3
3
,
,
,
,
log ,
, ,
2. 2. 2. 2. 2. ( )
( )
( )
( )
c r t
C
Log C Log
Log C Log Log
Log C
Anti soles
= = =
= +
=
=
= +
= +
=
=
3 500 0 07 5
3 500 1 0 07
3 500 1 07
3 500 5 1 07
3 54407 5 0 02938
3 54407 0 1469
3 69097
3 69097 4 908 94
5
5
. ,
. ,
. ,
. ,
, ,
, ,
log , . ,
3. 3. 3. 3. 3. ( )
( )
( )
( )
c r t
C
Log C Log
Log Log
Log C
Anti bs
= = =
= +
=
=
= +
= +
=
=
8 132 0 09 10
8 132 1 0 09
8 132 1 09
8 132 10 1 09
3 91020 10 0 03743
3 91020 0 3743
4 2845
4 2845 19 253 070
10
10
. ,
. ,
. ,
. ,
, ,
, ,
log , . , .
4. 4. 4. 4. 4. ( )
( )
( )
( )
c r t
C
Log C Log
Log Log
Log C Anti
= = =
= +
=
=
= +
= +
=
=
930 0 035 7
930 1 0 035
930 1 035
930 7 1 035
2 9684829 7 0 0149403
2 9684829 0 01045821
3 073065 3 073065 1 183 2186
7
7
,
,
,
,
, ,
, ,
log , $ . ,
5. 5. 5. 5. 5. ( )
( )
( )
C t
r
C
Log C Log
Log Log
Log C
Anti
= =
= = = ⇒ =
= +
=
=
= +
= +
=
=
12 318 6
4
17
4
4 25
4 25
100
0 0425
12 318 1 0 0425
12 318 1 0425
12 318 6 1 0425
4 0905402 6 0 018076
4 0905402 0 108456
4 1989962
4 1989962 15 812 34204
1
4
6
6
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