find value of log 256 to the base 64
Answers
Answer:
log
64
(
256
)
=
x
Rewrite the equation as
x
=
log
64
(
256
)
.
x
=
log
64
(
256
)
Logarithm base
64
of
256
is
4
3
.
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Rewrite as an equation.
log
64
(
256
)
=
x
Rewrite
log
64
(
256
)
=
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
.
64
x
=
256
Create expressions in the equation that all have equal bases.
(
2
6
)
x
=
2
8
Rewrite
(
2
6
)
x
as
2
6
x
.
2
6
x
=
2
8
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
6
x
=
8
Solve for
x
.
x
=
4
3
The variable
x
is equal to
4
3
.
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Factor
2
out of
8
.
x
=
2
(
4
)
6
Cancel the common factors.
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Factor
2
out of
6
.
x
=
2
⋅
4
2
⋅
3
Cancel the common factor.
x
=
2
⋅
4
2
⋅
3
Rewrite the expression.
x
=
4
3
The result can be shown in multiple forms.
Exact Form:
x
=
4
3
Decimal Form:
x
=
1.
¯
3
Mixed Number Form:
x
=
1
1
3
Answer:
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