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Question Number 180363 by peter frank last updated on 11/Nov/22

Answered by mr W last updated on 11/Nov/22

$$t=y^{\frac{1}{2}}$$$$y=t^2$$$${\left(\frac{2\log t}{\log 3}\right)}^2-\log t-\frac{3}{2}=0$$$$\log t=\frac{1\pm \sqrt{1+4\times \frac{4}{{\left(\log 3\right)}^2}\times \frac{3}{2}}}{\frac{8}{{\left(\log 3\right)}^2}}$$$$\log t=\frac{\log 3}{8}[\log 3\pm \sqrt{{\left(\log 3\right)}^2+24}]$$$$\Rightarrow y=t^2=e^{\frac{\log 3}{4}[\log 3\pm \sqrt{{\left(\log 3\right)}^2+24}]}$$

Commented by peter frank last updated on 11/Nov/22

$$\mathrm{thank}\mathrm{you}$$

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