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Mathematics
Mathematics
Problem
If
x
x
x
is a positive number different from 1, such that
log
a
x
\log_a x
lo
g
a
x
,
log
b
x
\log_b x
lo
g
b
x
and
log
c
x
\log_c x
lo
g
c
x
are in AP, then a.
log
b
=
2
(
log
a
)
(
log
c
)
(
log
a
+
log
c
)
\log b = \frac{2(\log a)(\log c)}{(\log a + \log c)}
lo
g
b
=
(
l
o
g
a
+
l
o
g
c
)
2
(
l
o
g
a
)
(
l
o
g
c
)
b.
b
=
a
+
c
2
b = \frac{a + c}{2}
b
=
2
a
+
c
c.
b
=
a
c
b = \sqrt{ac}
b
=
a
c
d.
c
2
=
(
a
c
)
log
a
b
c^2 = (ac)^{\log_a b}
c
2
=
(
a
c
)
l
o
g
a
b
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