第2章权限–练习2.2 |套装1
问题11.(5/3) -2应该乘以多少才能使乘积等于(7/3) -1 ?
解决方案:
Let the number be x
(5/3)-2 × x = (7/3)-1
1/(5/3)2 × x = 1/(7/3) (1/an = a-n)
x = (3/7) / (3/5)2
= (3/7) / (9/25)
= (3/7) × (25/9)
3 is the common factor
= (1/7) × (25/3)
= 25/21
问题12。找到x,如果
(i)(1/4) -4 ×(1/4) -8 =(1/4) -4倍
解决方案:
(1/4)-4 × (1/4)-8 = (1/4)-4x
(1/4)-4 – 8 = (1/4)-4x (an × am = an + m)
(1/4)-12 = (1/4)-4x
When the bases are same, exponents are equated
-12 = -4x
x = -12/-4
Transposing -4
= 3
(ii)(-1/2) -19 ÷(-1/2) 8 =(-1/2) -2x + 1
解决方案:
(-1/2)-19 ÷ (-1/2)8 = (-1/2)-2x + 1
(1/2)-19-8 = (1/2)-2x+1 (we know that an ÷ am = an – m)
(1/2)-27 = (1/2)-2x + 1
When the bases are same, exponents are equated
-27 = -2x + 1
Transposing 1
-2x = -27 – 1
-2x = -28
Transposing -2
x= -28/-2
= 14
(iii)(3/2) -3 ×(3/2) 5 =(3/2) 2倍+ 1
解决方案:
(3/2)-3 × (3/2)5 = (3/2)2x + 1
(3/2)-3+5 = (3/2)2x + 1 (an × am = an + m)
(3/2)2 = (3/2)2x + 1
When the bases are same, exponents are equated
2 = 2x + 1
Transposing 1
2x = 2 – 1
2x = 1
Transposing 2
x = 1/2
(iv)(2/5) -3 ×(2/5) 15 =(2/5) 2 + 3倍
解决方案:
(2/5)-3 × (2/5)15 = (2/5)2 + 3x
(2/5)-3+15 = (2/5)2 + 3x (an × am = an + m)
(2/5)12 = (2/5)2+3x
When the bases are same, exponents are equated
12 = 2 + 3x
Transposing 2
3x = 12 – 2
3x = 10
Transposing 3
x = 10/3
(v)(5/4) -x ÷(5/4) -4 =(5/4) 5
解决方案:
(5/4)-x ÷ (5/4)-4 = (5/4)5
(5/4)-x+4 = (5/4)5 (an ÷ am = an – m)
When the bases are same, exponents are equated
-x + 4 = 5
Transposing 4
-x = 5 – 4
-x = 1
x = -1
(vi)(8/3) 2x + 1 ×(8/3) 5 =(8/3) x + 2
解决方案:
(8/3)2x+1 × (8/3)5 = (8/3)x+2
(8/3)2x+1+5 = (8/3) x + 2 (an × am = an + m)
(8/3)2x+6 = (8/3) x+2
When the bases are same, exponents are equated
2x + 6 = x + 2
Transposing 6 and x
2x – x = -6 + 2
x = -4
问题13.(i)如果x =(3/2) 2 ×(2/3) -4 ,则求出x -2的值。
解决方案:
x = (3/2)2 × (2/3)-4
= (3/2)2 × (3/2)4 (1/an = a-n)
= (3/2)2 + 4 (an × am = an + m)
= (3/2)6
x-2 = ((3/2)6)-2
= (3/2)-12
= (2/3)12
(ii)如果x =(4/5) -2 ÷(1/4) 2 ,则找到x -1的值。
解决方案:
x = (4/5)-2 ÷ (1/4)2
= (5/4)2 ÷ (1/4)2 (1/an = a-n)
= (5/4)2 × (4/1)2
= 25/16 × 16
16 is the common factor
= 25
x-1 = 1/25
问题14.查找x的值,其中5 2x ÷5 -3 = 5 5
解决方案:
52x ÷ 5-3 = 55
52x + 3 = 55 (an ÷ am = an – m)
When the bases are same, exponents are equated
2x + 3 = 5
Transposing 3
2x = 5 – 3
2x = 2
Transposing 2
x = 1