3) Find the values of:
i) log(1/2)8
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Answer:
log
1
2
(
8
)
Rewrite as an equation.
log
1
2
(
8
)
=
x
Rewrite
log
1
2
(
8
)
=
x
in exponential form using the definition of a logarithm. If
x
and
b
are positive real numbers and
b
does not equal
1
, then
log
b
(
x
)
=
y
is equivalent to
b
y
=
x
.
(
1
2
)
x
=
8
Create expressions in the equation that all have equal bases.
(
2
−
1
)
x
=
2
3
Rewrite
(
2
−
1
)
x
as
2
−
x
.
2
−
x
=
2
3
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
−
x
=
3
Solve for
x
.
x
=
−
3
The variable
x
is equal to
−
3
.
−
3
Step-by-step explanation:
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