1: =>\(5^{2x-3}=5^2\cdot3+5^2\cdot2=5^2\cdot5=5^3\)

=>2x-3=3

=>2x=6

=>x=3

2: \(41-2^{x+1}=9\)

=>\(2^{x+1}=32\)

=>x+1=5

=>x=4

3: =>\(4^{x+2}=65-1=64\)

=>x+2=3

=>x=1

\(5^{2x-3}-2.5^2=5^2.3\\ 5^{2x-3}=5^2.3+5^2.2\\ 5^{2x-3}=5^2.\left(3+2\right)\\ 5^{2x-3}=5^2.5\\ 5^{2x-3}=5^3\\ \Rightarrow2x-3=3\\ 2x=3+3\\ 2x=6\\ x=\dfrac{6}{2}\\ Vậy:x=3\)

\(41-2^{x+1}=9\\ 2^{x+1}=41-9\\ 2^{x+1}=32=2^5\\ \Rightarrow x+1=5\\ \Leftrightarrow x=5-1=4\\ ---\\ 65-4^{x+2}=2014^0\\ 65-4^{x+2}=1\\ 4^{x+2}=65-1\\ 4^{x+2}=64=4^3\\ \Rightarrow x+2=3\\ Vậy:x=1\)

a, 1230 : 3(x – 20) = 10

3(x – 20) = 123

x – 20 = 41

x = 61

b, 250 – 10.(24 – 3x):15 = 244

10.(24 – 3x):15 = 6

10.(24 – 3x) = 90

24 – 3x = 9

3x = 15

x = 5

c,  4 x 3  + 15 = 47

4 x 3 = 32

x 3 = 8 = 2 3

x = 2

d,  65 - 4 x + 2 = 2014 0

65 - 4 x + 2 = 1

4 x + 2 = 64 = 4 3

x + 2 = 3

x = 1

e,  4 . 2 x - 3 = 125

4 . 2 x = 128

2 x = 32 = 2 5

x = 5

a. (15+37)+(52-37-17)  = 15+37+52-37-17
= 15+(37-37)+52-17
= 15+0+35
= 50

a) 52x - 3 - 2 . 52 = 52 . 3

x - 3/52 - 2 = 3

x = 3 + 2 + 3/52

x = 263/52

b) 740 / (x + 10) = 102 - 2 . 13

740 / (x + 10) = 76

x + 10 = 740 / 76

x + 10 = 185/19

x = 185/19 - 10

x = -5/19

c) 65 - 4x + 2 = 20140

65 - 4x = 20140 - 2

65 - 4x = 20138

4x = 65 - 20138

4x = -20073

x = -20073/4

d) 120 + 2 . (3x - 17) = 214

60 + 3 . x - 17 = 107

20 + x - 17/3 = 107/3

20 + x = 107/3 + 17/3

20 + x = 124/3

x = 124/3 - 20

x = 64/3

e) 41 - 2x + 1 = 9

42 - 2x = 9

21 - x = 9/2

x = 21 - 9/2

x = 33/2

khó đấy

ta có a=20140-(b+c); b=20140-(a+c); c=20140-(a+b) thay vào S ta được:\(S=\frac{20140-\left(b+c\right)}{b+c}+\frac{20140-\left(a+c\right)}{a+c}+\frac{20140-\left(a+b\right)}{a+b}=20140\left(\frac{1}{b+c}+\frac{1}{a+c}+\frac{1}{a+b}\right)-3=2011 \)