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Question Number 82125 by liki last updated on 18/Feb/20

Commented by john santu last updated on 18/Feb/20

$${\log }_y\left(x\right)=\frac{1}{{\log }_x\left(y\right)}$$$$\Rightarrow {\log }_y\left(x\right)+\frac{1}{{\log }_y\left(x\right)}=64$$$$p^2-64p+1=0,p={\log }_y\left(x\right)$$$${(p-32)}^2-1023=0$$$$p=32\pm \sqrt{1023}\Rightarrow p=\{\begin{array}{l}32+\sqrt{1023}\\ 32-\sqrt{1023}\end{array}$$

Commented by liki last updated on 18/Feb/20

$$..\mathit{h}\mathit{e}\mathit{l}\mathit{p}\mathit{m}\mathit{e}\mathit{p}\mathit{l}\mathit{z}...$$

Commented by liki last updated on 18/Feb/20

$$...\mathit{s}\mathit{o}\mathit{r}\mathit{y}\mathit{s}\mathit{i}\mathit{r},\mathit{a}\mathit{f}\mathit{t}\mathit{e}\mathit{r}\mathit{g}\mathit{e}\mathit{t}\mathit{t}\mathit{i}\mathit{n}\mathit{g}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathit{o}\mathit{f}\mathit{p}\mathit{h}\mathit{o}\mathit{w}\mathit{c}\mathit{a}\mathit{n}\mathit{t}\mathit{o}\mathit{o}\mathit{b}\mathit{t}\mathit{a}\mathit{i}\mathit{n}\mathit{x}\mathit{a}\mathit{n}\mathit{d}\mathit{y}?$$

Commented by liki last updated on 18/Feb/20

$$..oksirthankyou$$

Commented by mr W last updated on 18/Feb/20

$$youhavetwounknownsx,y$$$$butyouhaveonlyoneequation,in$$$$thiscaseyoucannotdeterminex$$$$andy!becausethereareinfinite$$$$possibilities.$$

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