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Problem 1 :
If x-1/3 = 5/2, then find the value of x.
Problem 2 :
If 42n + 3 = 8n + 5, then find the value of n.
Problem 3 :
If 5x/25y = 125, then solve for x in terms of y.
Problem 4 :
If ax = b, by = c and cz = a, then find the value of xyz.
Problem 5 :
If a and b are positive even integers, which of the following is greatest ?
A) (-2a)b
B) (-2a)2b
C) (2a)b
D) 2a2b
Problem 6 :
If √(x√x) = xa, then find the value of a.
Problem 7 :
If x2 = y3 and x3z = y9, then find the value of z.
Problem 8 :
If n3 = x, n4 = 20x and n > 0, then find the value of n.
Problem 9 :
If (√9)-7 ⋅ (√3)-4 = 3k, then find the value of k.
Problem 10 :
In the equation 2√(x - 2) = 3√2, if x ≥ 2, then find the value of x.
1. Answer :
x-1/3 = 5/2
x = (5/2)-3/1
x = (5/2)-3
x = (2/5)3
Distribute the exponent to numerator and denominator.
x = 23 / 53
x = 8/125
2. Answer :
42n + 3 = 8n + 5
(22)2n + 3 = (23)n + 5
22(2n + 3) = 23(n + 5)
Equate the exponents.
2(2n + 3) = 3(n + 5)
4n + 6 = 3n + 15
n = 9
3. Answer :
5x/25y = 125
5x/(52)y = 53
5x/52y = 53
5x - 2y = 53
x - 2y = 3
x = 2y + 3
4. Answer :
ax = b
Substitute a = cz.
(cz)x = b
czx = b
Substitute c = by.
(by)zx = b
bxyz = b
bxyz = b1
xyz = 1
5. Answer :
Because a and b are positive even integers, better we can assume some values for a and b and go through each choice.
Let a = 2 and b = 2.
Substitute a = 2 and b = 2 in each option.
A : [-2(2)]2 = (-4)2 = 16
B : [-2(2)]2(2) = (-4)4 = 256
C : [2(2)]2 = (4)2 = 16
D : 2(2)2(2) = 2(2)4 = 2(16) = 32
So, option B is the greatest.
6. Answer :
√(x√x) = xa
√(x ⋅ x1/2) = xa
√(x1 + 1/2) = xa
√(x3/2) = xa
(x3/2)1/2 = xa
x3/4 = xa
3/4 = a
7. Answer :
x3z = y9
x3z = y3(3)
x3z = (y3)3
Substitute x2 for y3.
x3z = (x2)3
x3z = x6
3z = 6
Divide each side by 3.
z = 2
8. Answer :
n4 = 20x
n3 ⋅ n = 20x
Substitute x for n3.
x ⋅ n = 20x
nx = 20x
Divide each side by x.
n = 20
9. Answer :
(91/2)-7 ⋅ (31/2)-4 = 3k
(9)-7/2 ⋅ (3)-4/2 = 3k
(32)-7/2 ⋅ 3-2 = 3k
32 ⋅ (-7/2) ⋅ 3-2 = 3k
3-7 ⋅ 3-2 = 3k
3-7 - 2 = 3k
3-9 = 3k
k = -9
10. Answer :
2√(x - 2) = 3√2
Square both sides to get rid of the radicals.
[2√(x - 2)]2 = (3√2)2
22 ⋅ [√(x - 2)]2 = 32 ⋅ (√2)2
4 ⋅ (x - 2) = 9 ⋅ 2
4x - 8 = 18
Add 8 to each side.
4x = 26
Divide each side by 4.
x = 6.5
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