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Question-186867




Question Number 186867 by Mingma last updated on 11/Feb/23
Answered by aba last updated on 11/Feb/23
x=−5  (1−(1/5))^(−4) =((5/4))^4 =(1+(1/4))^4
$${x}=−\mathrm{5} \\ $$$$\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{5}}\right)^{−\mathrm{4}} =\left(\frac{\mathrm{5}}{\mathrm{4}}\right)^{\mathrm{4}} =\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{4}} \\ $$
Commented by Mingma last updated on 11/Feb/23
Good!
Answered by aba last updated on 11/Feb/23
(1+(1/x))^(x+1) =(1+(1/4))^4 ⇒ (1+(1/x))^(x+1) =(1−(1/5))^(−5+1)   ⇒x=−5
$$\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}+\mathrm{1}} =\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{4}} \Rightarrow\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}+\mathrm{1}} =\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{5}}\right)^{−\mathrm{5}+\mathrm{1}} \\ $$$$\Rightarrow{x}=−\mathrm{5}\: \\ $$
Commented by Mingma last updated on 11/Feb/23
Good!

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