If b is any positive real number with b ≠ 1 and x is any real number, b − x is defined as follows: b − x = 1 b x Use this definition and the definition of logarithm to prove that log b ( 1 u ) = − log b ( u ) for all positive real numbers u and b, with b ≠ 1.
If b is any positive real number with b ≠ 1 and x is any real number, b − x is defined as follows: b − x = 1 b x Use this definition and the definition of logarithm to prove that log b ( 1 u ) = − log b ( u ) for all positive real numbers u and b, with b ≠ 1.
Solution Summary: The author explains how to determine the value of b-x by the definition of a logarithm.
If b is any positive real number with
b
≠
1
and x is any real number,
b
−
x
is defined as follows:
b
−
x
=
1
b
x
Use this definition and the definition of logarithm to prove that
log
b
(
1
u
)
=
−
log
b
(
u
)
for all positive real numbers u and b, with
b
≠
1.
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