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National and Regional Contests
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National High School Mathematics League
1998 National High School Mathematics League
1
Logarithm
Logarithm
Source: 1998 National High School Mathematics League, Exam One, Problem 1
March 8, 2020
logarithms
Problem Statement
If
a
>
1
,
b
>
1
,
lg
(
a
+
b
)
=
lg
a
+
lg
b
a>1,b>1,\lg(a+b)=\lg a+\lg b
a
>
1
,
b
>
1
,
l
g
(
a
+
b
)
=
l
g
a
+
l
g
b
, then the value of
lg
(
a
−
1
)
+
lg
(
b
−
1
)
\lg(a-1)+\lg(b-1)
l
g
(
a
−
1
)
+
l
g
(
b
−
1
)
is
(A)
lg
2
(B)
1
(C)
0
(D)
\text{(A)}\lg2\qquad\text{(B)}1\qquad\text{(C)}0\qquad\text{(D)}
(A)
l
g
2
(B)
1
(C)
0
(D)
not sure
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