Ta có: \(\frac{x^2}{6}=\frac{24}{25}\)

\(\Rightarrow x^2=24.6:25=5,76\)

\(\Rightarrow x=2,4\)

Vậy x = 2,4

a)  2^x-1 =16 => 2^x-1 = 2⁴ => x-1 =4 => x =5

b) (x-1 )² = 25 => (x-1)² = 5²  => x -1 =5 => x =5

                                              hoặc x-1 =-5 => x =-4

a) 2^x-1=16

2^x-1=2^4

=>x-1=4

=>x=4+1

=>x=5

b)(x-1)^2=25

=>(x-1)^2=5^2

=>x-1=5

=>x=5+1

=>x=6

hoặc  x-1=-5

=>x=-5+1

=>x=-4

Với x = 25, ta có :

E = x⁷ - 26x⁶ + 27x⁵ - 47x⁴ - 77x³ + 50x² + x - 24

=> E = x⁷ - (x +1)x⁶ + (x + 2)x⁵ - (2x - 3)x⁴ - (3x + 2)x³ + 2x. x² - x - (x - 1)

=> E = x⁷ - x⁷ - x⁶ + x⁶ + 2x⁵ - 2x⁵ + 3x⁴ - 3x⁴ - 2x³ + 2x³ - x - x + 1

=> E = -2x + 1

Thay x = 25 vào E :

E = -2 . 25 + 1 = -50 + 1 = -49

\(\frac{\sqrt{49}}{6}< \left|x-\frac{2}{3}\right|< \frac{26}{\sqrt{81}}\)

\(\Rightarrow\frac{7}{6}< \left|x-\frac{2}{3}\right|< \frac{26}{9}\)

\(\Rightarrow\frac{21}{18}< \left|x-\frac{12}{18}\right|< \frac{52}{18}\)

còn lại cậu tự tính nha

\(\frac{\sqrt{49}}{6}< \left|x-\frac{2}{3}\right|< \frac{26}{\sqrt{81}}\)

\(\frac{7}{6}< x-\frac{2}{3}< \frac{26}{9}\)

\(\frac{11}{6}< x< \frac{32}{9}\)

\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^x\)

\(\Rightarrow\frac{4.4^5}{3.3^5}.\frac{6.6^5}{2.2^5}=2^x\)

\(\Rightarrow\frac{4^6}{3^6}.\frac{6^6}{2^6}=2^x\)

\(\Rightarrow\frac{4^6.6^6}{3^6.2^6}=2^x\)

\(\Rightarrow\frac{\left(4.6\right)^6}{\left(3.2\right)^6}=2^x\)

\(\Rightarrow\frac{24^6}{6^6}=2^x\)

\(\Rightarrow4^6=2^x\)

\(\Rightarrow\left(2^2\right)^6=2^x\)

\(\Rightarrow2^{2.6}=2^x\)

\(\Rightarrow2^{12}=2^x\)

\(\Rightarrow x=12\)

\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^x.\)

\(\Rightarrow\frac{4.4^5}{3.3^5}.\frac{6.6^5}{2.2^5}=2^x\)\(\Rightarrow\frac{4^6.6^6}{3^6.2^6}=2^x\)

\(\Rightarrow\frac{2^6.2^6.2^6.3^6}{3^6.2^6}=2^x\)\(\Rightarrow2^6.2^6=2^x\)

\(\Rightarrow2^{12}=2^x\Leftrightarrow x=12\)

\(x=2,4\)

X = 3 

hok tốt

x= 12/5 hoặc x=-12/5

\(\frac{x^2}{6}=\frac{24}{25}\)

\(x^2\cdot25=6\cdot24\)

\(x^2\cdot25=144\)

\(x^2=144:25\)

\(x=\pm\sqrt{\frac{12}{5}}\)

Ta có:

\(\frac{x^2}{6}=\frac{24}{25}\Leftrightarrow x^2.25=24.6\)

\(\Leftrightarrow x^2=\frac{24.6}{25}=\frac{144}{25}=5,76\)

\(\Leftrightarrow x=\sqrt{5,76}=2,4;x=-\sqrt{5,76}=-2,4\)

Vậy \(x=2,4\) hoặc \(x=-2,4\)