MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1957 AMC 12/AHSME
28
28
Part of
1957 AMC 12/AHSME
Problems
(1)
Dependency of a Logarithm
Source:
6/8/2009
If
a
a
a
and
b
b
b
are positive and a\not\equal{} 1,\,b\not\equal{} 1, then the value of
b
log
b
a
b^{\log_b{a}}
b
l
o
g
b
a
is:
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
dependent upon
b
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
dependent upon
a
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
dependent upon
a
and
b
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
zero
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
one
<span class='latex-bold'>(A)</span>\ \text{dependent upon }{b} \qquad <span class='latex-bold'>(B)</span>\ \text{dependent upon }{a}\qquad <span class='latex-bold'>(C)</span>\ \text{dependent upon }{a}\text{ and }{b}\qquad <span class='latex-bold'>(D)</span>\ \text{zero}\qquad <span class='latex-bold'>(E)</span>\ \text{one}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
dependent upon
b
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
dependent upon
a
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
dependent upon
a
and
b
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
zero
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
one
logarithms