How do I solve x^ln x = 3^9 ?

1 Answer
Rhys
Apr 23, 2018

#=>x = e^( 3sqrt(ln3) ) #

Explanation:

Use your log laws...

#ln alpha ^ beta = beta ln alpha #

Take #ln# both sides...

#=> lnx^(lnx) = ln3^9 #

#=> lnx * lnx = 9ln3 #

#=> (lnx)^2 = 9ln3 #

#=> lnx = 3 sqrt(ln3) #

#=> e^(lnx) = e^( 3sqrt(ln3) ) #

#=>x = e^( 3sqrt(ln3) ) #

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