a) \(12.4+225:\left(x-3\right)^2=37\)

\(48+225:\left(x^2-6x+9\right)=37\)

\(48+\frac{225}{x^2}-\frac{225}{6x}+\frac{225}{9}=37\)

\(48+\frac{15}{x}-\frac{37,5}{x}+25=37\)

\(48-\frac{22,5}{x}+25=37\)

\(\frac{-22,5}{x}=37-25-48\)

\(\frac{-22,5}{x}=-36\)

\(x=-22,5:-36\)

\(x=\frac{5}{8}\)

vậy \(x=\frac{5}{8}\)

b) \(2x-138=2^3.3^2\)

\(2x-138=72\)

\(2x=72+138\)

\(2x=210\)

\(x=105\)

vậy \(x=105\)

b,2 nhân x - 138 =72

2 nhân x =72 + 138

2 nhân x =210

x =210 : 2

x =105

\(46-6\left(x-3\right)=2^3.5\)

\(\Rightarrow46-6\left(x-3\right)=40\)

\(\Rightarrow6\left(x-3\right)=6\)

\(\Rightarrow x-3=1\Rightarrow x=4\)

giúp mình với mình đang cần gấp

\(\Rightarrow4^x=4^4:4^3=4^1\\ \Rightarrow x=1\)

⇒ 4^x . 4³ = 4⁴

⇒ x + 3 = 4

⇒ x       = 1

\(5871:\left[928-\left(247-82.5\right)\right]\)

\(=5871:\left[928-\left(247-460\right)\right]\)

\(=5871:\left[928-\left(-213\right)\right]\)

\(=5871:1141\)

a) 2

b) 8

 a) 26- 3(X+1)  = 17

          3(X+1)  =  26 - 17

           3(X+1) =   9

              X+1  = 9: 3

              X+1   =  3

               X      =  3- 1

        Vậy:X      =2

 b) 5X -8 =  2³. 2²

     5X - 8 = 8 .  4

     5X  - 8 = 32

        5X    =32+8

         5X   =    40

           X   =  40 :5

    Vậy  X   =  8

 Trung Thu vui vẻ nha mn

a:2

b:8

chuc trung thu vui ve nha

\(4^x=4^3.4^5\Rightarrow x=3+5=8\)

\(2^x=8.128\Rightarrow2^x=2^3.2^7\Rightarrow x=3+7=10\)

\(4^X=4^3.4^5\)

\(4^X\)=\(4^7\)

\(\Rightarrow\)X=7

\(2^X=8.128\)

\(2^X=2^3.2^7\)

\(2^X\)=\(2^{10}\)

\(\Rightarrow\)x=10

chú ý: dấu nhân kí hiệu là .

4^x=4³.4⁵

4^x=4³⁺⁵

4^x=4⁸

<=> x=8

2^x=8.128

2^x=2³.2⁷

2^x=2³⁺⁷

2^x=2¹⁰

<=> x=10

#)Giải ;

b) Đặt \(N=1+2+2^2+2^3+...+2^{2012}\)

\(\Rightarrow2N=2+2^2+2^3+2^4+...+2^{2013}\)

\(\Rightarrow2N-N=N=\left(2+2^2+2^3+2^4+...+2^{2013}\right)-\left(1+2+2^2+2^3+...+2^{2012}\right)\)

\(\Rightarrow N=2^{2013}-1\)

Thay N vào M, ta có :

\(M=\frac{2^{2013}-1}{2^{2014}-2}\)

Thêm Cho pen 

\(M=\frac{2^{2013}-1}{2^{2014}-2}=\frac{2^{2013}-1}{2.\left(2^{2013}-1\right)}=\frac{1}{2}\)

Phải tính  hết nhé

a, \(A=\frac{24\cdot47-23}{24+47-23}\cdot\frac{3+\frac{3}{7}-\frac{3}{11}+\frac{3}{1001}-\frac{3}{13}}{\frac{9}{1001}-\frac{9}{13}+\frac{9}{7}-\frac{9}{11}+9}\)

\(A=\frac{24\cdot47-23}{24+47-23}\cdot\frac{3.\left(1+\frac{1}{7}-\frac{1}{11}+\frac{1}{1001}-\frac{1}{13}\right)}{9.\left(1+\frac{1}{7}-\frac{1}{11}+\frac{1}{1001}-\frac{1}{13}\right)}\)

\(A=\frac{24\cdot47-23}{24+47-23}\cdot\frac{3}{9}\)

\(A=\frac{1105}{48}\cdot\frac{1}{3}=\frac{1105}{144}\)

Vậy A = \(\frac{1105}{144}\)

b, Đặt A = 1 + 2 + 2^2 + 2^3 + ... + 2^2012 

2A = 2(1 + 2 + 2^2 + 2^3 + ... + 2^2012) 

2A = 2 + 2^2 + 2^3 + 2^4 + ... + 2^2012 

2A - A = (2 + 2^2 + 2^3 + 2^4 + ... + 2^2012) - (1 + 2 + 2^2 + 2^3 + ... + 2^2012) 

A = 2^2012 - 1 

=> M = \(\frac{2^{2012}-1}{2^{2014}-2}=\frac{2^{2012}-1}{2^{2014}-2}=\frac{2^{2012}-1}{2.2.\left(2^{2012}-1\right).}=0,25\)

Vậy M = 0,25