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Question Number 174292 by akolade last updated on 29/Jul/22

$$\frac{\log (\sqrt{\mathrm{x}+1}+1)}{{\log }^3\sqrt{\mathrm{x}-40}}=3$$$$\mathrm{find}\mathrm{x}$$

Answered by Rasheed.Sindhi last updated on 29/Jul/22

$$\frac{\log (\sqrt{\mathrm{x}+1}+1)}{{\log }^3\sqrt{\mathrm{x}-40}}=3$$$$\log (\sqrt{\mathrm{x}+1}+1)={3\log }^3\sqrt{\mathrm{x}-40}$$$$\log (\sqrt{\mathrm{x}+1}+1)=\log {\left({}^3\sqrt{\mathrm{x}-40}\right)}^3$$$$\sqrt{\mathrm{x}+1}+1=\mathrm{x}-40$$$$\sqrt{\mathrm{x}+1}=\mathrm{x}-41$$$$\mathrm{x}+1={(\mathrm{x}-41)}^2$$$${\mathrm{x}}^2-82\mathrm{x}+1681=\mathrm{x}+1$$$${\mathrm{x}}^2-83\mathrm{x}+1680=0$$$$\mathrm{x}=48,35$$

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