Treball1 Mat1
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ACTIVITAT sobre Equacions exponencials i logarítmiques. Sistemes Resoleu: 1) 3x+2 + 3x+1 + 3x = 117
2)
5x - 5x-1 + 25x = 1/5
3)
2x+1 + 4x-1 = 96
4)
5x = 3x+1
5)
2x+2 + 6·2x+1 -4 = 0
6)
2logx – 1 =log4x
7)
log(3x+5) + 1 = log(3x-2)
8)
log(x+5) – log(x-3) = 2
9)
ln(x+2) + lnx = ln(x-8)2
10)
logx – log8 = log(x+5) - log2
11)
log(x+3) – log(x+1) = 1 – log5
12)
7 x − 6·2 y = 1 7 x − 2 y = 41
13)
log x + log y = 1 2 log x = log( y 2 + 21)
14)
2x +3y = 5 5·2 x − 4·3 y = 16
15)
log y ( x − 12) = 2 1 log x ( y + 1) = 2
16)
log( x + y ) + log( x − y ) = log 13 ln e x = ln e y +1
Solucions:
1) x = 2 2) x = -1 3) x = 4 6) x = 40 7) x = -52/27 (no val) 9) x = 32/9 10) x = -20/3 (no val) 13) x1=5 y1=2 , x2=-5 y2=-2 15) x=169/4 y= 11/2
4) x = 2’15 5) x= -2 8) x = 305/99 11) x = 1 12) x=2 y=3 14) x=2 y=0 16) x=7 y=6
2)
5x - 5x-1 + 25x = 1/5
3)
2x+1 + 4x-1 = 96
4)
5x = 3x+1
5)
2x+2 + 6·2x+1 -4 = 0
6)
2logx – 1 =log4x
7)
log(3x+5) + 1 = log(3x-2)
8)
log(x+5) – log(x-3) = 2
9)
ln(x+2) + lnx = ln(x-8)2
10)
logx – log8 = log(x+5) - log2
11)
log(x+3) – log(x+1) = 1 – log5
12)
7 x − 6·2 y = 1 7 x − 2 y = 41
13)
log x + log y = 1 2 log x = log( y 2 + 21)
14)
2x +3y = 5 5·2 x − 4·3 y = 16
15)
log y ( x − 12) = 2 1 log x ( y + 1) = 2
16)
log( x + y ) + log( x − y ) = log 13 ln e x = ln e y +1
Solucions:
1) x = 2 2) x = -1 3) x = 4 6) x = 40 7) x = -52/27 (no val) 9) x = 32/9 10) x = -20/3 (no val) 13) x1=5 y1=2 , x2=-5 y2=-2 15) x=169/4 y= 11/2
4) x = 2’15 5) x= -2 8) x = 305/99 11) x = 1 12) x=2 y=3 14) x=2 y=0 16) x=7 y=6
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