MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
1998 National Olympiad First Round
2
2
Part of
1998 National Olympiad First Round
Problems
(1)
(2^1998)(5^1998)
Source: 0
4/23/2009
Let
A
A
A
,
B
B
B
be the number of digits of
2
1998
2^{1998}
2
1998
and
5
1998
5^{1998}
5
1998
in decimal system. A \plus{} B \equal{} ?
<
s
p
a
n
c
l
a
s
s
=
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l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
1998
<
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l
a
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=
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−
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>
(
B
)
<
/
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p
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>
1999
<
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c
l
a
s
s
=
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a
t
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x
−
b
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>
(
C
)
<
/
s
p
a
n
>
2000
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
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>
(
D
)
<
/
s
p
a
n
>
3996
<
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a
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=
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x
−
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>
(
E
)
<
/
s
p
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>
3998
<span class='latex-bold'>(A)</span>\ 1998 \qquad<span class='latex-bold'>(B)</span>\ 1999 \qquad<span class='latex-bold'>(C)</span>\ 2000 \qquad<span class='latex-bold'>(D)</span>\ 3996 \qquad<span class='latex-bold'>(E)</span>\ 3998
<
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=
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x
−
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>
(
A
)
<
/
s
p
an
>
1998
<
s
p
an
c
l
a
ss
=
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a
t
e
x
−
b
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d
′
>
(
B
)
<
/
s
p
an
>
1999
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
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l
d
′
>
(
C
)
<
/
s
p
an
>
2000
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
3996
<
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p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
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l
d
′
>
(
E
)
<
/
s
p
an
>
3998
floor function
logarithms