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Math Problems
Grade 8
Solve equations with variable exponents
Solve for
x
x
x
.
7
7
7
3
=
7
x
\frac{7^7}{7^3} = 7^x
7
3
7
7
=
7
x
\newline
x
=
x =
x
=
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Solve for
x
x
x
.
1
1
x
1
1
3
=
1
1
2
\frac{11^x}{11^3} = 11^2
1
1
3
1
1
x
=
1
1
2
\newline
x
=
x =
x
=
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486
486
486
+
108
108
108
x +
6
6
6
x^
2
2
2
=
\newline
A)
6
6
6
(x+
9
9
9
)^
2
2
2
\newline
B)
6
6
6
(x
−
9
-9
−
9
)^
2
2
2
\newline
C)
6
6
6
(x+
6
6
6
)^
2
2
2
\newline
D)
6
6
6
(x
−
6
-6
−
6
)^
2
2
2
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if
2
a
=
2
5
7
2^a=\sqrt[7]{2^5}
2
a
=
7
2
5
what is the value of
a
a
a
?
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How does
h
(
x
)
=
4
x
h(x)=4^x
h
(
x
)
=
4
x
change over the interval from
x
=
8
x=8
x
=
8
to
x
=
10
x=10
x
=
10
?
\newline
Choices:
\newline
h(x) increases by a factor of 16
\text{h(x) increases by a factor of 16}
h(x) increases by a factor of 16
\newline
h(x) increases by a factor of 8
\text{h(x) increases by a factor of 8}
h(x) increases by a factor of 8
\newline
h(x) decreases by a factor of 16
\text{h(x) decreases by a factor of 16}
h(x) decreases by a factor of 16
\newline
h(x) decreases by a factor of 8%
\text{h(x) decreases by a factor of 8\%}
h(x) decreases by a factor of 8%
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Solve for
r
r
r
.
\newline
7
r
=
49
7^r = 49
7
r
=
49
\newline
r
=
_
_
_
r = \_\_\_
r
=
___
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Solve for
q
q
q
.
\newline
1
0
q
=
1
,
000
10^q = 1,000
1
0
q
=
1
,
000
\newline
q
=
_
_
_
q = \_\_\_
q
=
___
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Solve for
w
w
w
.
\newline
1
0
w
=
10
,
000
10^w = 10,000
1
0
w
=
10
,
000
\newline
w = ____
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Solve for
u
u
u
.
\newline
9
u
=
81
9^u = 81
9
u
=
81
\newline
u
=
_
_
_
u = \_\_\_
u
=
___
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Solve for
r
r
r
.
\newline
1
0
r
=
100
,
000
10^r = 100,000
1
0
r
=
100
,
000
\newline
r
=
_
_
_
r = \_\_\_
r
=
___
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Solve for
z
z
z
.
\newline
2
z
=
4
2^z = 4
2
z
=
4
\newline
z
=
_
_
_
z = \_\_\_
z
=
___
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Solve for
r
r
r
.
\newline
3
r
=
27
3^r = 27
3
r
=
27
\newline
r
=
_
_
_
r = \_\_\_
r
=
___
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Solve for
d
d
d
.
\newline
1
0
d
=
100
10^d = 100
1
0
d
=
100
\newline
d
=
_
_
_
d = \_\_\_
d
=
___
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Solve for
z
z
z
.
\newline
6
z
=
36
6^z = 36
6
z
=
36
\newline
z
=
_
_
_
z = \_\_\_
z
=
___
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Solve for
b
b
b
.
\newline
2
b
=
8
2^b = 8
2
b
=
8
\newline
b
=
_
_
_
b = \_\_\_
b
=
___
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How do I solve
l
o
g
(
6.
5
x
+
25.2
0
x
)
=
x
+
l
o
g
25
?
log(6.5^x+25.20^x)=x+log 25 ?
l
o
g
(
6.
5
x
+
25.2
0
x
)
=
x
+
l
o
g
25
?
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Solve for
x
x
x
:
2
x
=
32
2^{x}=32
2
x
=
32
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If
7
a
=
7
3
7^a=\sqrt[3]{7}
7
a
=
3
7
, what is the value of
a
a
a
?
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In the following equation, what is the value of
n
n
n
?
\newline
8
n
=
8
−
3
×
8
7
8^n = 8^{-3} \times 8^7
8
n
=
8
−
3
×
8
7
\newline
n
=
n =
n
=
____
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Solve for
s
s
s
.
\newline
6
s
=
36
6^s = 36
6
s
=
36
\newline
s
=
s =
s
=
____
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Solve for
u
u
u
.
\newline
8
u
=
64
8^u = 64
8
u
=
64
\newline
u
=
_
_
_
u = \_\_\_
u
=
___
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Solve for
w
w
w
.
\newline
9
w
=
81
9^w = 81
9
w
=
81
\newline
w
w
w
= ____
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Solve for
y
y
y
.
\newline
7
y
=
49
7^y = 49
7
y
=
49
\newline
y
y
y
= ____
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Solve for
s
s
s
.
\newline
1
0
s
=
100
10^s = 100
1
0
s
=
100
\newline
s
=
s =
s
=
____
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Solve for
w
w
w
.
\newline
5
w
=
25
5^w = 25
5
w
=
25
\newline
w
w
w
= ____
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Solve for
p
p
p
.
\newline
1
0
p
=
1
,
000
10^p = 1,000
1
0
p
=
1
,
000
\newline
p
=
_
_
_
p = \_\_\_
p
=
___
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Solve for
s
s
s
.
\newline
2
s
=
4
2^s = 4
2
s
=
4
\newline
s
s
s
= ____
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Solve for
b
b
b
.
\newline
3
b
=
9
3^b = 9
3
b
=
9
\newline
b
b
b
= ____
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Solve for
q
q
q
.
\newline
3
q
=
27
3^q = 27
3
q
=
27
\newline
q
q
q
= ____
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What is
2
,
000
×
h
for
h
=
0.002
2,000 \times h \text{ for } h = 0.002
2
,
000
×
h
for
h
=
0.002
.
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solve this equation:
9
x
+
1
+
1
=
10
(
3
x
)
9^x+1 + 1 = 10(3^x)
9
x
+
1
+
1
=
10
(
3
x
)
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What is the value of
2
69420
2^{69420}
2
69420
?
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60
2
−
12
×
2
\frac{60}{2} - 12 \times 2
2
60
−
12
×
2
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1
1
+
e
−
7
\frac{1}{1+e^{-7}}
1
+
e
−
7
1
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If
2
a
=
2
5
7
2^a=\sqrt[7]{2^5}
2
a
=
7
2
5
, what is the value of
a
a
a
?
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x
2
−
1
=
0
x^2-1=0
x
2
−
1
=
0
, solve for
x
x
x
.
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solve for
x
x
x
6
4
x
−
9
=
(
1
36
)
x
−
4
6^{4x-9}=(\frac{1}{36})^{x-4}
6
4
x
−
9
=
(
36
1
)
x
−
4
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if
3
a
=
5
3
4
3^a=5\sqrt{3^4}
3
a
=
5
3
4
,what is the value of
a
a
a
?
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If
1
1
a
=
4
1
1
3
11^a = 4\sqrt{11^3}
1
1
a
=
4
1
1
3
, what is the value of
a
a
a
?
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If
1
1
a
=
4
1
1
3
11^a = 4\sqrt{11^3}
1
1
a
=
4
1
1
3
, what is the value of
a
a
a
?
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Factor the expression completely.
\newline
x
y
+
x
3
y
x y+x^{3} y
x
y
+
x
3
y
\newline
Answer:
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Factor the expression completely.
\newline
y
−
x
5
y
y-x^{5} y
y
−
x
5
y
\newline
Answer:
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Factor the expression completely.
\newline
x
−
x
3
y
x-x^{3} y
x
−
x
3
y
\newline
Answer:
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Factor the expression completely.
\newline
x
2
y
−
x
5
x^{2} y-x^{5}
x
2
y
−
x
5
\newline
Answer:
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Factor the expression completely.
\newline
30
x
−
24
30 x-24
30
x
−
24
\newline
Answer:
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Factor the expression completely.
\newline
24
x
+
15
24 x+15
24
x
+
15
\newline
Answer:
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Solve for x.
8
7
=
8
3
⋅
8
x
8^7 = 8^3 \cdot 8^x
8
7
=
8
3
⋅
8
x
x = __
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