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Math Problems
Precalculus
Change of base formula
Evaluate the expression:
\newline
1
−
0.36
+
2
−
0.56
+
3
−
0.75
=
\sqrt{1-0.36}+\sqrt{2-0.56}+\sqrt{3-0.75}=
1
−
0.36
+
2
−
0.56
+
3
−
0.75
=
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Simplify the expression. Write your answers using integers or improper fractions.
\newline
−
(
2
r
−
1
4
r
+
3
)
−
r
-\left(2 r-\frac{1}{4} r+3\right)-r
−
(
2
r
−
4
1
r
+
3
)
−
r
\newline
Answer:
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Simplify the expression. Write your answers using integers or improper fractions.
\newline
−
2
(
3
m
+
5
)
−
8
5
m
-2(3 m+5)-\frac{8}{5} m
−
2
(
3
m
+
5
)
−
5
8
m
\newline
Answer:
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2
+
2
×
2
=
2+2\times 2=
2
+
2
×
2
=
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Express the given expression as an integer or as a fraction in simplest form.
\newline
(
1
0
log
10
+
log
7
)
\left(10^{\log 10+\log 7}\right)
(
1
0
l
o
g
10
+
l
o
g
7
)
\newline
Answer:
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Solve for
c
c
c
. Express your answer as a proper or improper fraction in simplest terms.
\newline
−
2
5
c
+
3
4
=
2
5
-\frac{2}{5} c+\frac{3}{4}=\frac{2}{5}
−
5
2
c
+
4
3
=
5
2
\newline
Answer:
c
=
c=
c
=
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Solve for
y
y
y
. Express your answer as a proper or improper fraction in simplest terms.
\newline
−
1
2
−
4
9
y
=
1
8
-\frac{1}{2}-\frac{4}{9} y=\frac{1}{8}
−
2
1
−
9
4
y
=
8
1
\newline
Answer:
y
=
y=
y
=
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Solve for
x
x
x
. Express your answer as a proper or improper fraction in simplest terms.
\newline
−
3
4
x
+
1
3
=
−
1
5
-\frac{3}{4} x+\frac{1}{3}=-\frac{1}{5}
−
4
3
x
+
3
1
=
−
5
1
\newline
Answer:
x
=
x=
x
=
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Simplify to a single power of
6
6
6
:
\newline
6
7
6
5
\frac{6^{7}}{6^{5}}
6
5
6
7
\newline
Answer:
6
□
6 ^\square
6
□
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Write the expression
3
ln
3
−
2
ln
5
3 \ln 3-2 \ln 5
3
ln
3
−
2
ln
5
as a single logarithm in simplest form without any negative exponents.
\newline
Answer:
ln
(
□
)
\ln (\square)
ln
(
□
)
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Write the expression
ln
2
+
ln
3
\ln 2+\ln 3
ln
2
+
ln
3
as a single logarithm in simplest form without any negative exponents.
\newline
Answer:
ln
(
□
)
\ln (\square)
ln
(
□
)
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Write the expression
3
ln
3
−
ln
5
3 \ln 3-\ln 5
3
ln
3
−
ln
5
as a single logarithm in simplest form without any negative exponents.
\newline
Answer:
ln
(
□
)
\ln (\square)
ln
(
□
)
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Write the expression
2
ln
2
−
ln
3
2 \ln 2-\ln 3
2
ln
2
−
ln
3
as a single logarithm in simplest form without any negative exponents.
\newline
Answer:
ln
(
□
)
\ln (\square)
ln
(
□
)
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A culture of bacteria starts with
50
50
50
bacteria and increases exponentially.
\newline
The relationship between
B
B
B
, the number of bacteria in the culture, and
d
d
d
, the elapsed time, in days, is modeled by the following equation.
\newline
B
=
50
⋅
1
0
d
2
B=50 \cdot 10^{\frac{d}{2}}
B
=
50
⋅
1
0
2
d
\newline
In how many days will the number of bacteria in the culture reach
800
800
800
,
000
000
000
?
\newline
Give an exact answer expressed as a base-ten logarithm.
\newline
days
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Rewrite as a quotient of two common logarithms. Write your answer in simplest form.
\newline
log
5
7
=
\log_5 7 =
lo
g
5
7
=
______
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