log-p-q-x-2-log-q-p-3-x-find-x-

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

{\begin{cases} \log_{p} (q) = x^{2} \\ \log_{q} (p^{3}) = x \end{cases}

f i n d x

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

{\begin{cases} q = p^{x^{2}} \to q^{x} = {(p^{x^{2}})}^{x} \\ p^{3} = q^{x} \to p^{3} = p^{x . x^{2}} \end{cases}

\Rightarrow x^{3} = 3; x = \sqrt[3]{3} (J S ⊛)

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

{l o g}_{p} (q) = x^{2}

3 {l o g}_{q} (p) = x

3 {l o g}_{q} p . {l o g}_{p} q = x^{3}

3 = x^{3}

x = \sqrt[3]{3}