Question

решите уравнение log2(x)+logx(2)=2,5

Answer 1

loga (b) = 1 / logb (a)
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log2(x) +1/log2 (x) =2,5   (x>0)
y = log2 (x)
y+1/y =2,5
y² -2,5y +1=0
D=6,25 - 4 =2,25   √D=1,5
y1=(2,5+1,5)/2=2     y2=(2,5-1,5)/2=1/2
log2 x=2   x1=4
log2 x =1/2     x2=√2