ln x= 4logx (e), solve for x

If this is meant to be ln(x) = 4*log_x(e)  (i.e. log to base x of e) then

 

ln(x) = log_x(e⁴)

x^ln(x) = e⁴

 

Take log to base e of both sides

ln(x^ln(x)) = ln(e⁴)

ln(x)*ln(x) = 4

[ln(x)]² = 4

ln(x) = ±2

x = e² and x = e^-2

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