If x^x = 27^x+27 find x {x}^(x) = {27}^(x + 27) ​

Question

If x^x = 27^x+27 find x

`{x}^(x) = {27}^(x + 27)`
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Answer 1

`x^x=27^(x+27)\\\ln x^x=\ln (27^(x+27))\\x\ln x=(x+27)\ln27\\x\ln x=x\ln 27+27\ln 27\\x\ln x-x\ln 27=27\ln 27\\\ln x-\ln 27=(27\ln 27)/(x)\\\ln(x)/(27)=(27\ln 27)/(x)\\(x)/(27)=e^{(27\ln 27)/(x)}\\\ln 27=(27\ln 27)/(x)e^{(27\ln 27)/(x)}\\(27\ln 27)/(x)=W(\ln27)\\x=(27\ln 27)/(W(\ln 27))=81`