the value of log base3,3cube under root
Answers
Evaluate ( log base 3 of 3 square root of 3)/( cube root of 3)
log 3(3√3)
3√3
Multiply
log 3(3√3)
3√3
by
3√3
23√3A2
.
log
3
(
3
√
3
)
3
√
3
⋅
3
√
3
2
3
√
3
2
Combine and simplify the denominator.
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Multiply
log
3
(
3
√
3
)
3
√
3
and
3
√
3
2
3
√
3
2
.
log
3
(
3
√
3
)
3
√
3
2
3
√
3
3
√
3
2
Raise
3
√
3
to the power of
1
.
log
3
(
3
√
3
)
3
√
3
2
3
√
3
1
3
√
3
2
Use the power rule
a
m
a
n
=
a
m
+
n
to combine exponents.
log
3
(
3
√
3
)
3
√
3
2
3
√
3
1
+
2
Add
1
and
2
.
log
3
(
3
√
3
)
3
√
3
2
3
√
3
3
Rewrite
3
√
3
3
as
3
.
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Rewrite
3
√
3
as
3
1
3
.
log
3
(
3
√
3
)
3
√
3
2
(
3
1
3
)
3
Apply the power rule and multiply exponents,
(
a
m
)
n
=
a
m
n
.
log
3
(
3
√
3
)
3
√
3
2
3
1
3
⋅
3
Combine
1
3
and
3
.
log
3
(
3
√
3
)
3
√
3
2
3
3
3
Cancel the common factor of
3
.
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log
3
(
3
√
3
)
3
√
3
2
3
1
Evaluate the exponent.
log
3
(
3
√
3
)
3
√
3
2
3
Simplify the numerator.
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Rewrite
3
√
3
2
as
(
3
2
)
1
3
.
log
3
(
3
√
3
)
3
√
3
2
3
Raise
3
to the power of
2
.
log
3
(
3
√
3
)
3
√
9
3
Rewrite
log
3
(
3
√
3
)
using the change of base formula.
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The change of base rule can be used if
a
and
b
are greater than
0
and not equal to
1
, and
x
is greater than
0
.
log
a
(
x
)
=
log
b
(
x
)
log
b
(
a
)
3
√
9
3
Substitute in values for the variables in the change of base formula, using
b
=
10
.
log
(
3
√
3
)
log
(
3
)
3
√
9
3
Combine
log
(
3
√
3
)
log
(
3
)
and
3
√
9
.
log
(
3
√
3
)
3
√
9
log
(
3
)
3
Multiply the numerator by the reciprocal of the denominator.
log
(
3
√
3
)
3
√
9
log
(
3
)
⋅
1
3
Multiply
log
(
3
√
3
)
3
√
9
log
(
3
)
⋅
1
3
.
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Multiply
log
(
3
√
3
)
3
√
9
log
(
3
)
and
1
3
.
log
(
3
√
3
)
3
√
9
log
(
3
)
⋅
3
Reorder
log
(
3
)
and
3
.
log
(
3
√
3
)
3
√
9
3
⋅
log
(
3
)
Simplify
3
⋅
log
(
3
)
by moving
3
inside the logarithm.
log
(
3
√
3
)
3
√
9
log
(
3
3
)
Raise
3
to the power of
3
.
log
(
3
√
3
)
3
√
9
log
(
27
)
The result can be shown in multiple forms.
Exact Form:
log
(
3
√
3
)
3
√
9
log
(
27
)
Decimal Form:
1.04004191
…