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Question Number 104835 by bemath last updated on 24/Jul/20

$$\{\begin{array}{l}\log {}_p\left(q\right)=x^2\\ \log {}_q\left(p^3\right)=x\end{array}$$$$findx$$

Answered by john santu last updated on 24/Jul/20

$$\{\begin{array}{l}q=p^{x^2}\to q^x={\left(p^{x^2}\right)}^x\\ p^3=q^x\to p^3=p^{x.x^2}\end{array}$$$$\Rightarrow x^3=3;x=\sqrt[3]{3}(JS⊛)$$

Answered by Dwaipayan Shikari last updated on 24/Jul/20

$${log}_p\left(q\right)=x^2$$$$3{log}_q\left(p\right)=x$$$$3{log}_{q}p.{log}_{p}q=x^3$$$$3=x^3$$$$x=\sqrt[3]{3}$$

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