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GEvS
@GEvS
December 2021
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Решите уравнение log 37 по основанию х, минус log x^2 по основанию 37 равно -1
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Анатоле
Verified answer
Logx(37) - 2log37(x) = -1
1/log37(x) - 2 log37(x) = -1
2log37(x)^2 - log37(x) - 1 = 0
t = log37(x)
2t^2 - t - 1 = 0
D = 1 + 8 = 9
t1 = (1+3)/4 = 1
t2 = (1-3)/4 = -1/2
log37(x) = 1 x = 37
log37(x) = -1/2 x = 1/корень(37)
3 votes
Thanks 2
mikael2
Verified answer
Log37 x=z
1/z-2z+1=0
-2z²+z+1=0
2z²-z-1=0
z1=1 log37 x=1 x=37
z2=-0.5 log37 x=-0.5 x=1/√37
1 votes
Thanks 1
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Answers & Comments
Verified answer
Logx(37) - 2log37(x) = -11/log37(x) - 2 log37(x) = -1
2log37(x)^2 - log37(x) - 1 = 0
t = log37(x)
2t^2 - t - 1 = 0
D = 1 + 8 = 9
t1 = (1+3)/4 = 1
t2 = (1-3)/4 = -1/2
log37(x) = 1 x = 37
log37(x) = -1/2 x = 1/корень(37)
Verified answer
Log37 x=z1/z-2z+1=0
-2z²+z+1=0
2z²-z-1=0
z1=1 log37 x=1 x=37
z2=-0.5 log37 x=-0.5 x=1/√37