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Solve for x: \(\ln \left( x \frac { 1 } { \ln \left( x \frac{ 1 } { \ln \left( x \frac { 1 } { \ln \left( x \cdot \cdot \cdot \right) } \right) } \right) } \right) = \mathrm{e}\)

 Jun 26, 2020
 #1
avatar+25541 
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Solve for x:
\(\ln \left( x \dfrac { 1 } { \ln \left( x \dfrac{ 1 } { \ln \left( x \dfrac { 1 } { \ln \left( x \cdot \cdots \right) } \right) } \right) } \right) = \mathrm{e}\)

 

\(\begin{array}{|rcll|} \hline e &=& \ln\left(x*\dfrac{1}{e}\right) \\\\ e^e &=& \dfrac{x}{e} \\\\ e^ee &=& x \\ x &=& e^ee \\ \mathbf{x} &=& \mathbf{e^{e+1}} \\ \mathbf{x} &=& \mathbf{41.1935556747} \\ \hline \end{array}\)

 

laugh

 Jun 26, 2020

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