SOLUTION: Solve for x: e^x = 5 e^e^x = 2 (e to the e to the x)

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Question 144824: Solve for x:
e^x = 5
e^e^x = 2
(e to the e to the x)
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
e%5Ex=5 Start with the given equation


ln%28e%5Ex%29=ln%285%29 Take the natural of both sides


x%2Aln%28e%29=ln%285%29 Rewrite the left side using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


x=ln%285%29 Take the natural log of e to get 1



So our answer is x=ln%285%29 which is approximately x=1.60944
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e%5Ee%5Ex=2 Start with the given equation


ln%28e%5Ee%5Ex%29=ln%282%29 Take the natural log of both sides


e%5Ex%2Aln%28e%29=ln%282%29 Rewrite the left side using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


e%5Ex=ln%282%29 Take the natural log of e to get 1


ln%28e%5Ex%29=ln%28ln%282%29%29 Take the natural log of both sides again


x%2Aln%28e%29=ln%28ln%282%29%29 Rewrite the left side using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


x=ln%28ln%282%29%29 Take the natural log of e to get 1


So our answer is x=ln%28ln%282%29%29 which is approximately x=-0.36651