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5
x
=
5
5 x=5
5
x
=
5
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Math Problems
Precalculus
Solve logarithmic equations with multiple logarithms
Full solution
Q.
5
x
=
5
5 x=5
5
x
=
5
Divide by
5
5
5
:
Divide both sides by
5
5
5
to isolate x;
5
x
5
=
5
5
\frac{5x}{5} = \frac{5}{5}
5
5
x
=
5
5
Simplify to
x
=
1
x=1
x
=
1
:
Simplifying gives
x
=
1
x = 1
x
=
1
More problems from Solve logarithmic equations with multiple logarithms
Question
Solve. Write your answer as an integer or a fraction in simplest form.
\newline
5
x
=
1
5^x=1
5
x
=
1
\newline
x
=
x=
x
=
_____
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Posted 2 months ago
Question
Steven opened a savings account and deposited
$
100.00
\$100.00
$100.00
as principal. The account earns
9
%
9\%
9%
interest, compounded annually. What is the balance after
5
5
5
years?
\newline
Use the formula
A
=
P
(
1
+
r
n
)
n
t
A = P(1 + \frac{r}{n})^{nt}
A
=
P
(
1
+
n
r
)
n
t
, where
A
A
A
is the balance (final amount),
P
P
P
is the principal (starting amount),
r
r
r
is the interest rate expressed as a decimal,
n
n
n
is the number of times per year that the interest is compounded, and
t
t
t
is the time in years.
\newline
Round your answer to the nearest cent.
\newline
$
\$
$
____
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Posted 2 months ago
Question
Use the following function rule to find
f
(
1
)
f(1)
f
(
1
)
.
\newline
f
(
x
)
=
12
(
7
)
x
+
8
f(x) = 12(7)^x + 8
f
(
x
)
=
12
(
7
)
x
+
8
\newline
f
(
1
)
=
f(1) =
f
(
1
)
=
_____
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Posted 1 month ago
Question
The town of Valley View conducted a census this year, which showed that it has a population of
1
,
800
1,800
1
,
800
people. Based on the census data, it is estimated that the population of Valley View will grow by
12
%
12\%
12%
each decade.
\newline
Write an exponential equation in the form
y
=
a
(
b
)
x
y = a(b)^x
y
=
a
(
b
)
x
that can model the town population,
y
y
y
,
x
x
x
decades after this census was taken.
\newline
Use whole numbers, decimals, or simplified fractions for the values of
a
a
a
and
b
b
b
.
\newline
y
=
y =
y
=
______
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Posted 2 months ago
Question
Solve. Round your answer to the nearest thousandth.
\newline
7
=
9
x
7 = 9^x
7
=
9
x
\newline
x
=
x =
x
=
____
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Posted 2 months ago
Question
Solve. Round your answer to the nearest thousandth.
\newline
7
=
e
x
7 = e^x
7
=
e
x
\newline
x
=
x =
x
=
____
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Posted 1 month ago
Question
Solve. Simplify your answer.
\newline
log
u
=
1
\log u = 1
lo
g
u
=
1
\newline
u
=
u =
u
=
____
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Posted 2 months ago
Question
Solve. Simplify your answer.
\newline
7
log
x
=
7
7\log x = 7
7
lo
g
x
=
7
\newline
x
=
x =
x
=
____
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Posted 1 month ago
Question
How does
g
(
t
)
=
3
t
g(t) = 3^t
g
(
t
)
=
3
t
change over the interval from
t
=
3
t = 3
t
=
3
to
t
=
4
t = 4
t
=
4
?
\newline
Choices:
\newline
(A)
g
(
t
)
g(t)
g
(
t
)
decreases by
3
3
3
\newline
(B)
g
(
t
)
g(t)
g
(
t
)
increases by
3
3
3
\newline
(C)
g
(
t
)
g(t)
g
(
t
)
decreases by
3
%
3\%
3%
\newline
(D)
g
(
t
)
g(t)
g
(
t
)
increases by
200
%
200\%
200%
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Posted 2 months ago
Question
A function
f
(
x
)
f(x)
f
(
x
)
increases by
6
6
6
over every unit interval in
x
x
x
and
f
(
0
)
=
0
f(0) = 0
f
(
0
)
=
0
.
\newline
Which could be a function rule for
f
(
x
)
f(x)
f
(
x
)
?
\newline
Choices:
\newline
(A)
f
(
x
)
=
6
x
f(x) = 6^x
f
(
x
)
=
6
x
\newline
(B)
f
(
x
)
=
6
x
f(x) = 6x
f
(
x
)
=
6
x
\newline
(C)
f
(
x
)
=
1
6
x
f(x) = \frac{1}{6^x}
f
(
x
)
=
6
x
1
\newline
(D)
f
(
x
)
=
x
6
f(x) = \frac{x}{6}
f
(
x
)
=
6
x
Get tutor help
Posted 2 months ago
