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Logaritmická rovnice


MinecraftPlayer

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logx + 3/logx = 4                   /*logx

(logx)^2 + 3 = 4*logx            /-4*logx

(logx)^2 - 4*logx + 3 = 0      logx = a

a^2 - 4a + 3 = 0

 

D = (-4)^2 - 4*3*1 = 16 - 12 = 4

 

a1,2 = (4 +- 2)/2

a1 = 1

a2 = 3

 

logx = 1

x1 = 10

 

logx = 3

x2 = 1000

 

Koreny rovnice jsou 10 a 1000.

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