为什麽log(a)(x+b/x-b)=y可化得x=b(a的y次方+1)/a的y次方-1

为什麽log(a)(x+b/x-b)=y可化得x=b(a的y次方+1)/a的y次方-1
为什麽log(a)(x+b/x-b)=y可化得x=b(a的y次方+1)/a的y次方-1

为什麽log(a)(x+b/x-b)=y可化得x=b(a的y次方+1)/a的y次方-1
aˇy=(x+b)/(x-b)
aˇy * (x-b)=x+b
aˇy * x - aˇy * b = x+b
aˇy * x - x = b+ aˇy * b
x * (aˇy - 1)= b * (1 + aˇy)
x=b * (1 + aˇy)/(aˇy - 1)

y=loga[(x+b)/(x-b)]
a^y=(x+b)/(x-b)=1+2b/(x-b)
2b/(x-b)=a^y-1
x-b=2b/(a^y-1)
x=2b/(a^y-1)+b=[b(a^y-1)+2b]/(a^y-1)=b(a^y+1)/(a^y-1)

log(a)(x+b/x-b)=y
a^y=(x+b)/(x-b)
(a^y)*(x-b)=x+b
(a^y)x-(a^y)b=x+b
x=b[(a^y)+1]/(a^y-1)
y=loga[(x+b)/(x-b)]
a^y=(x+b)/(x-b)=1+2b/(x-b)
2b/(x-b)=a^y-1
x-b=2b/(a^y-1)
x=2b/(a^y-1)+b=[b(a^y-1)+2b]/(a^y-1)=b(a^y+1)/(a^y-1)

log(a) (x+b/x-b)=y
所以aˇy=(x+b)/(x-b) 其中aˇy表示a的y次方
所以aˇy * (x-b)=x+b
aˇy * x - aˇy * b = x+b
aˇy * x - x = b+ aˇy * b
x * (aˇy - 1)= b * (1 + aˇy)
x=b * (1 + aˇy)/(aˇy - 1)

假设ay表示a的y次方
ay=x+b/x-b
ay(x-b)=x+b
ay x-ay b=x+b
ay x-x=b+ay b
x(ay-1)=b(ay+1)
x=b(ay+1)/(ay-1)

log(a)(x+b/x-b)=y
a^y=(x+b)/(x-b)
(a^y)*(x-b)=x+b
(a^y)x-(a^y)b=x+b
x=b[(a^y)+1]/(a^y-1)