SOLUTION: log(e^2^(x+2))=2 The question is what is x closest too

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Question 658274: log(e^2^(x+2))=2
The question is what is x closest too
Answer by lwsshak3(11628) About Me  (Show Source):
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log(e^2^(x+2))=2
The question is what is x closest too
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log(100)=2
log(e^2^(x+2))=log(100)
(e^2^(x+2)=100
take log of both sides
(2^(x+2)lne=ln100
lne=1
2^(x+2)=ln100
take log of both sides again
(x+2)log2=log(ln100)
x+2=log(ln100)/log2≈2.2033
x≈2.2033-2
x≈.2033
check:
2^(x+2)=2^(2.2033)=4.6053
e^4.6053≈100
log(e^2^(x+2))=log100=2