1. No category

ECUACIONES IRRACIONALES
1.
2.
5x + 6 = 3 + 2x
x + 7 − 3x = 1
x = −1, x = − 3
4
x = −3
3.
2 − 5x + x 3 = 0
x = −2
4.
2x + 3 + x − 5 = 0
No tiene solución
5.
2x + 5x − 6 = 4
x=2
6.
7x + 1 = 5x − 7
4
6
x=5
7.
x−2 + x+1 = 3
x=3
8.
− 2x − 3 + 1 = x
No tiene solución
9.
2− x = x
x=1
10.
2x − 3 − x + 7 = 4
x = 114
11.
2+x = x
x=2
12.
3x + 3 − 1 =
13.
3x + 5x + 1 = 7
8 − 2x
x=2
x=3
ECUACIONES EXPONENCIALES
1.
2 x ⋅ 2 x+1 = 8
x=1
2.
5 ⋅ 7 −x = 35
3 3x−2 = 81
3 x+3
2 x ⋅ 5 x = 0, 1
4 x−1 = 186
2 x+2
3 x + 3 x+2 = 30
x = −1
x= 9
2
x = −1
3.
4.
5.
6.
x = 4 + ln 186 ≃ 11, 54
ln 2
x=1
8.
5 x+1 + 5 x + 5 x−1 = 31
5
x−1
x
x+1
2 +2 +2 = 7
9.
2 x + 2 x+1 + 2 x+2 + 2 x+3 = 480 x = 5
7.
10. 5 2x − 30 ⋅ 5 x + 125 = 0
x=1
x=1
12. 3 2x+2 − 28 ⋅ 3 x + 3 = 0
x = 1, x = 2
x = 1 ,x = 0
3
x = 1, x = −2
13. 4 x − 5 ⋅ 2 x + 4 = 0
x = 1, x = 4
11. 8 2x − 3 ⋅ 8 x + 2 = 0
1
ECUACIONES LOGARÍTMICAS
1.
log3x − 1 − log2x + 3 = 1 − log 25 x = 1
2.
log x 3 = log 6 + log x
log16 − x 2 
=2
log3x − 4
x = 12
5
4.
2 log x − logx − 16 = 2
x = 20, x = 80
5.
2 log x − logx + 6 = 3 log 2
x = 12
6.
log2x + 3 = logx + 5x − 3
x = 2, x = 3
7.
2logx = log5x − 6
x = 2, x = 3
3.
2
x=
2
2 log7x − 9 + 2 log3x − 4 = 2
9. log5x + 4 − log 2 = 1 logx + 4
2
10. 4logx = 2logx + log4 + 2
8.
6
x=2
x=0
x = 20
11. log2x − 3 + log3x − 2 = 2 − log25 x = 2
12. log x = 1 + log21 − x
x = 20
2
x=4
13. log10 − x − 1 = log 2x − 37
5
2