a: =>3(x+4)=115

=>x+4=115/3

hay x=103/3

b: =>\(8^3\cdot\left(12x-64\right)=4\cdot8^4\)

\(\Leftrightarrow12x-64=32\)

=>12x=96

hay x=8

c: \(\Leftrightarrow\left(4x+28\right)\cdot23+55=175\)

=>(4x+28)x23=120

=>4x+28=120/23

=>4x=-524/23

hay x=-131/23

1) \(\frac{25}{12}.x+\frac{11}{15}=\frac{9}{10}\)

=> \(\frac{25}{12}.x=\frac{9}{10}-\frac{11}{15}\)

=> \(\frac{25}{12}.x=\frac{1}{6}\)

=> \(x=\frac{1}{6}:\frac{25}{12}\)

=> \(x=\frac{2}{25}\)

Vậy \(x=\frac{2}{25}\).

3) \(\frac{29}{12}.\left[x\right]-\frac{5}{6}=\frac{3}{8}\)

=> \(\frac{29}{12}.\left[x\right]=\frac{3}{8}+\frac{5}{6}\)

=> \(\frac{29}{12}.x=\frac{29}{24}\)

=> \(x=\frac{29}{24}:\frac{29}{12}\)

=> \(x=\frac{1}{2}\)

Vậy \(x=\frac{1}{2}\).

4) \(\left[4x+\frac{3}{4}\right]-\frac{5}{4}=2\)

=> \(\left[4x+\frac{3}{4}\right]=2+\frac{5}{4}\)

=> \(4x+\frac{3}{4}=\frac{13}{4}\)

=> \(4x=\frac{13}{4}-\frac{3}{4}\)

=> \(4x=\frac{5}{2}\)

=> \(x=\frac{5}{2}:4\)

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

Vậy \(x=\frac{5}{8}\).

5) 2^x + 2^x+3 = 144

⇔ 2^x + 2^x . 2³ = 144

⇔ 2^x . (1 + 2³) = 144

⇔ 2^x . 9 = 144

⇔ 2^x = 144 : 9

⇔ 2^x = 16

⇔ 2^x = 2⁴

=> x = 4

Vậy x = 4.

Chúc bạn học tốt!

a) 3x^3-12x=0

3x(x^2-4)=0

3x(x-2)(x+2)=0

suy ra 3x=0       suy ra x=0

           x-2=0               x=2

           x+2=0              x= -2

b) (x-3)^2-(x-3)(3-x)^2=0

(x-3)^2-(x-3)(x-3)^2=0

(x-3)^2(1-x+3)=0

(x-3)^2(4-x)=0

suy ra x-3=0  suy ra x=3

          4-x=0             x=4

a) và b) đã nhé bạn

\(\left(12x-4\right)^3.8^3=4^{16}.16^3\)

\(\Leftrightarrow8\left(12x-4\right)^3=4^6.\left(4^2\right)^{^3}\)

\(\Leftrightarrow\left(96x-32\right)^3=4^6.4^6\)

\(\Leftrightarrow\left(96x-32\right)^3=16^6\)

\(\Leftrightarrow\left(96x-32\right)^3=\left(16^2\right)^{^3}\)

\(\Leftrightarrow\left(96x-32\right)^3=256^3\)

\(\Leftrightarrow96x-32=256\)

\(\Leftrightarrow x=\frac{256+32}{96}\)

Vậy \(x=3\)

(12x-4)³.8³=4³.16³

<=> [(12x-4).8]³=(4.16)³

=> (12x-4).8=4.16

<=> 12x-4=8

<=> 12x=12

=> x=1

\(\frac{8^{10}+4^{10}}{8^{11}+4^{11}}=\frac{2^{30}+2^{20}}{2^{33}+2^{22}}=\frac{2^{20}.\left(2^{10}+1\right)}{2^{20}.\left(2^{13}+2^2\right)}=\frac{2^{10}+1}{2^{13}+4}=\frac{1025}{8196}\)

Bài 12: 

\(\dfrac{a}{b}=\dfrac{7}{8}\)

nên \(b=a:\dfrac{7}{8}=\dfrac{8}{7}a\)

Ta có: \(\dfrac{b}{c}=\dfrac{4}{3}\)

\(\Leftrightarrow b=\dfrac{4}{3}c\)

\(\Leftrightarrow a\cdot\dfrac{8}{7}=\dfrac{4}{3}c\)

\(\Leftrightarrow a=\dfrac{4}{3}:\dfrac{8}{7}\cdot c=\dfrac{4}{3}\cdot\dfrac{7}{8}\cdot c=\dfrac{7}{6}c\)

Vậy: c tỉ lệ với a theo hệ số tỉ lệ k=6/7