Løsning af eksponentielle ligninger

Eksponentielle ligninger

3?·?2,4x = 12?·?0,8x

2,40,8x=123

3x=4

x·ln3x=4

x=ln4ln3=1,26

y=3·2,41,26=9,04

x,y=(1.26,9.04)

15?·?1,3x = 7?·?1,6x

1,61,3x=157

1,23x=2,14

x·ln1,23x=2,14

x=ln2,14ln1,23= 3,69

y=15·1,33,69=39,49

x,y=(3.69, 39.49)

1,5?·?3x = 0,2?·?1,5x

31,5x=1,50,2

2x=7,5

x·ln2x=7,5

x=ln7,5ln2=2,90

y=1,5·32,90=36,28

x,y=(2.90,36.28)

3?·?0,51x = 8?·?0,3x

0,,510,3x=83

1,7x=2,66

x·ln1,7x=2,66

x=ln2,66ln1,7=1,84

y=3·0,511,84=0,86

x,y=(1.84,0.86)

0,25?·?1,74x = 3,71?·?0,22x

1,740,22x=3,710,25

7,90x=14,84

x·7,90x=14,84

x=14,847,90=1,87

y=0,25·1,741,87=0,70

x,y=(1.87,0.70)

4,8?·?0,39x = 50?·?1,20x

1,200,39x=504,8

3,07x=10,41

x·3,07x=10,41

x=10,413,07=3,39

y=4,8·0,393,39=0,19

x,y=(3.39,0,19)