1º bachillerato ecuaciones logarítmicas, neperianas y exponenciales
TRANSCRIPT
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ECUACIONES ECUACIONES LOGARÍTMICAS
2
3
2
14
2
12
2
12262log
2
13log22log2
2log62log3log2log2log2log9log4
1log64log
232
22
12
32
26
22322
=−=−=−−−=−−
−=−−+=−−+ −
9
13513log32log51log3log2log1log27
1log
32
1log 322
33
52232
−=
=−−−=−−−=−+=−+ −−
6
1
32
1
32
12
32
11
log3
log2
11
log3
log2
1log1
log
loglog
log
log1
log
3
2
11
3
−=
−
=
=
+−
=+−
=
+−=
+−=+=
+ −
a
a
a
aa
a
aa
a
aa
22
1
2
125,0
2
125,0log
2
2
1 =→
=
→=
→= yyyy
310100001,0100001,0log 3 −=→=→=→= − yx yy ECUACIONES NEPERIANAS
511
ln 555
−=→=→=→= − yeee
eye
yy
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5
2
5
2lnln
5
2ln5ln2ln25ln2ln25ln
2
12ln4ln
44444 =→
=→
=−=−=−= xxx
( ) ( ) 4.15244.1484454ln 5554ln =+=+=→=−→=→=− − exexeex x
( )( )
64.01
44.0ln3
31.1ln
31.1ln331.1ln3
931.1ln
3
318631.1ln
3
263
2ln5ln3
2ln6ln35ln
3
2ln62lnln5lnln6
2ln
44.044.0ln
33 23
≈=→=→−=→−
=→
→=−→=
−→=
+−→=
+−
→−=+−→=+−−→=+−
−
exeexx
xxxx
xxxxxxxxx
x
ECUACIONES EXPONENCIALES
2445122322 22511 22
±=±=→=→=+→=→= ++ xxxxx
( ) 422555
15
25
15 2
2
2
1
2
12
2
2
1
=→−=
→−=→=→=→= − xxxxxx
→=+−→=→= +−+− 0653313 206565 22
xxxxxx
( ) ( )
=++=
=−==→±=−±=
−−±−−=→=+−
32
15
22
15
2
15
2
24255
1·2
6·1·455065
2
12
2
x
xxxx
65,05,0325,0 6 =→=→= xxx Descomposición factorial de 32:
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( )
3333*
277
1891897
9
189
9
3921
93
213·3·213·33·3321333
3
2132121
=→=→=
==→=→=+−→=−−
→=+− →=+−→=+− −−=−−−−
xy
yyyyyyy
y
yyy
xx
yxxxxxx x
22242
4123122122·2212222
211
=→=→==→=→=+ →=+→=+ =+
x
yyyyxx
yxxxx x
( ) →=++ →=++→=+− = 045042·52042·52 2222 yyyxxxx x
( ) ( )
=++=
=−==→±=−±=
−−±−−=→=+−
=+−
∗
∗
42
35
12
35
2
35
2
16255
1·2
4·1·455045
045
2
12
2
2
y
yyyy
yy
Si y =1 02212 0 =→=→=→ xxx Si y =4 22242 2 =→=→=→ xxx