Upper level math question?

Question

How would I solve this equation: e^e^x=10? This should be read as "e" to the "e to the x" power equals ten. Thanks.

Answer 1

What is the opposite of an exponential? That is right, it is the natural log. So your answer is x = ln(ln(10)) whatever that is as a decimal.

Answer 2

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Answer 3

Take then natural log ln, the inverse of e of both sides twice in succession. then

ln (ln x)= ln (ln 10) =x=.834

Answer 4

the answer is 0 because ln10=1
ln 1=0
therefore ln(ln(10))=ln(1)=0

Answer 5

Use the rule of logs and exponents, which says:

ln (e^a) = a * ln e = a

e^(e^x) = 10

ln e^(e^x) = ln 10
e^x * ln e = ln 10
e^x * 1 = ln 10

Then:
e^x = ln 10
ln e^x = ln (ln 10)
x * ln e = ln (ln 10)
x * 1 = ln (ln 10)
x = ln (ln 10)

Answer 6

take the natural log of each side twice. that will give you

x = ln[ ln[10] ]

Answer 7

i don't no cause im in 3-4th grade

Answer 8

helixburger is right.