log root 9 to the base 1/9
Answers
Answer:
Step-by-step explanation:
log
9
(
√
3
)
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
)
Substitute in values for the variables in the change of base formula, using
b
=
10
.
log
(
√
3
)
log
(
9
)
The result can be shown in multiple forms.
Exact Form:
log
(
√
3
)
log
(
9
)
Decimal Form:
0.25
Answer:
-1
Step-by-step explanation:
Rewrite as an equation.
log 9 ( 1 9 ) = x Rewrite log 9 ( 1 9 ) = 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 . 9 x = 1 9
Create expressions in the equation that all have equal bases.
( 3 2 ) x = 3 − 2 Rewrite ( 3 2 ) x as 3 2 x . 3 2 x = 3 2
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
2
x = − 2
Solve for
x . = − 1
The variable
x
is equal to
− 1