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4
Math Prize 2011 Problem 4
Math Prize 2011 Problem 4
Source:
September 19, 2011
logarithms
Problem Statement
If
x
>
10
x > 10
x
>
10
, what is the greatest possible value of the expression
(
log
x
)
log
log
log
x
−
(
log
log
x
)
log
log
x
?
{( \log x )}^{\log \log \log x} - {(\log \log x)}^{\log \log x} ?
(
lo
g
x
)
l
o
g
l
o
g
l
o
g
x
−
(
lo
g
lo
g
x
)
l
o
g
l
o
g
x
?
All the logarithms are base 10.
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