log 4 to the base 3 × log of 81 to the base 4
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Answer:
Rewrite as an equation.
log 4 ( log 3 ( 81) = x
)
Rewrite
log
3
(
81
)
=
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
.
log
4
(
3
x
=
81
)
Create equivalent expressions in the equation that all have equal bases.
log
4
(
3
x
=
3
4
)
Since the bases are the same, the two expressions are only equal if the exponents are also equal.
log
4
(
x
=
4
)
The variable
x
is equal to
4
.
log
4
(
4
)
Logarithm base
4
of
4
is
1
.
Step-by-step explanation:
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