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MAA AMC
AMC 12/AHSME
1970 AMC 12/AHSME
8
Logarithm Manipulations
Logarithm Manipulations
Source: 1970 AHSME Problem 8
March 21, 2014
logarithms
AMC
Problem Statement
If
a
=
log
8
225
a=\log_8225
a
=
lo
g
8
225
and
b
=
log
2
15
b=\log_215
b
=
lo
g
2
15
, then
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
a
=
1
2
b
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
a
=
2
b
3
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
a
=
b
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
b
=
1
2
a
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
a
=
3
b
2
<span class='latex-bold'>(A) </span>a=\frac{1}{2}b\qquad<span class='latex-bold'>(B) </span>a=\frac{2b}{3}\qquad<span class='latex-bold'>(C) </span>a=b\qquad<span class='latex-bold'>(D) </span>b=\frac{1}{2}a\qquad <span class='latex-bold'>(E) </span>a=\frac{3b}{2}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
a
=
2
1
b
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
a
=
3
2
b
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
a
=
b
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
b
=
2
1
a
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
a
=
2
3
b
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