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Question Number 146355 by bemath last updated on 13/Jul/21

$$\mathrm{If}{3}^{4^{2^x}}={81}^{2^6}\mathrm{then}\sqrt{x^2+5}=?$$

Answered by iloveisrael last updated on 13/Jul/21

$$\iff 3^{4^{2^{\mathrm{x}}}}={81}^{2^6}$$$$\iff 3^{4^{2^{\mathrm{x}}}}=3^{4.2^6}$$$$\iff 4^{2^{\mathrm{x}}}=4.2^6=4.4^3$$$$\Rightarrow 4^{2^{\mathrm{x}}}=4^4$$$$\Rightarrow 2^{\mathrm{x}}=4;\mathrm{x}=2$$$$\iff \sqrt{{\mathrm{x}}^2+5}=\sqrt{4+5}=3$$

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