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Question Number 67025 by Masumsiddiqui399@gmail.com last updated on 21/Aug/19

Commented by Rasheed.Sindhi last updated on 22/Aug/19

x^x^(x+5)  =^3 (√3)  (x^x^(x+5)  )^3 =(^3 (√3))^3   x^(3x^(x+5) ) =3  x^(3x^(x+5) ) .3^(x+5) =3.3^(x+5)   x^(3x^(x+5) +x+5) =3^(x+6)   ....

$${x}^{{x}^{{x}+\mathrm{5}} } =\:^{\mathrm{3}} \sqrt{\mathrm{3}} \\ $$$$\left({x}^{{x}^{{x}+\mathrm{5}} } \right)^{\mathrm{3}} =\left(\:^{\mathrm{3}} \sqrt{\mathrm{3}}\right)^{\mathrm{3}} \\ $$$${x}^{\mathrm{3}{x}^{{x}+\mathrm{5}} } =\mathrm{3} \\ $$$${x}^{\mathrm{3}{x}^{{x}+\mathrm{5}} } .\mathrm{3}^{{x}+\mathrm{5}} =\mathrm{3}.\mathrm{3}^{{x}+\mathrm{5}} \\ $$$${x}^{\mathrm{3}{x}^{{x}+\mathrm{5}} +{x}+\mathrm{5}} =\mathrm{3}^{{x}+\mathrm{6}} \\ $$$$.... \\ $$

Commented by mr W last updated on 22/Aug/19

Rasheed sir:  please have a look at Q66832. any  idea for an easier way to solve?  thanks sir!

$${Rasheed}\:{sir}: \\ $$$${please}\:{have}\:{a}\:{look}\:{at}\:{Q}\mathrm{66832}.\:{any} \\ $$$${idea}\:{for}\:{an}\:{easier}\:{way}\:{to}\:{solve}? \\ $$$${thanks}\:{sir}! \\ $$

Commented by Rasheed.Sindhi last updated on 22/Aug/19

Sir I think that ′chinese remainder theorm′  is most proper way.However you have done  it in a creative way!

$${Sir}\:{I}\:{think}\:{that}\:'{chinese}\:{remainder}\:{theorm}' \\ $$$${is}\:{most}\:{proper}\:{way}.{However}\:{you}\:{have}\:{done} \\ $$$${it}\:{in}\:{a}\:{creative}\:{way}! \\ $$

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