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Let’s check out your problem:
log
x
(
1
81
)
=
−
3
\log_{x}(\frac{1}{81}) = -3
lo
g
x
(
81
1
)
=
−
3
View step-by-step help
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Math Problems
Precalculus
Convert between exponential and logarithmic form
Full solution
Q.
log
x
(
1
81
)
=
−
3
\log_{x}(\frac{1}{81}) = -3
lo
g
x
(
81
1
)
=
−
3
Convert to Exponential Form:
Step
1
1
1
: Convert the logarithmic equation to an exponential form.
log
x
(
1
81
)
=
−
3
\log_{x}(\frac{1}{81}) = -3
lo
g
x
(
81
1
)
=
−
3
can be rewritten as
x
−
3
=
1
81
x^{-3} = \frac{1}{81}
x
−
3
=
81
1
.
Simplify Using Exponents:
Step
2
2
2
: Simplify the equation using properties of exponents.
x
−
3
=
1
81
x^{-3} = \frac{1}{81}
x
−
3
=
81
1
implies that
(
1
x
3
)
=
1
81
.
(\frac{1}{x^3}) = \frac{1}{81}.
(
x
3
1
)
=
81
1
.
Solve for
x
3
x^3
x
3
:
Step
3
3
3
: Solve for
x
3
x^3
x
3
.
\newline
Taking the reciprocal of both sides, we get
x
3
=
81
x^3 = 81
x
3
=
81
.
Find Cube Root of
81
81
81
:
Step
4
4
4
: Find the cube root of
81
81
81
to solve for
x
x
x
.
\newline
x
=
8
1
1
/
3
x = 81^{1/3}
x
=
8
1
1/3
.
\newline
Since
81
=
3
4
81 = 3^4
81
=
3
4
, then
x
=
(
3
4
)
1
/
3
=
3
4
/
3
x = (3^4)^{1/3} = 3^{4/3}
x
=
(
3
4
)
1/3
=
3
4/3
.
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