1 ) x = 0,375

2) x= 7,530514717

nhoc oi tra loi han hoi ra

a) \(2^{3x+2}=4^{x+5}\Leftrightarrow2^{3x+2}=2^{2\left(x+5\right)}\Leftrightarrow2^{3x+2}=2^{2x+10}\)

\(\Rightarrow3x+2=2x+10\Leftrightarrow3x+2-2x-10\)

\(\Leftrightarrow x-8=0\Leftrightarrow x=8\) vậy \(x=8\)

câu : b ; c mk cảm thấy đề sai

\(2^1.2^2.2^3.....2^x=1024\Rightarrow2^{1+2+3+...+x}=2^{10}\)

\(\Rightarrow1+2+3+...+x=1024\Rightarrow x=4\)

a, 1 x 2 x 3 x ... x 8 x 9 - 1 x 2 x 3 x ... x 8 - 1 x 2 x 3 x ... x 7 x 8 x 8 

= 1 x 2 x 3 x ... x 8 ( 9 - 1 - 8 ) = 1 x2 x 3 x ... x 8 . 0 = 0 

Bài post của vuong hien duc

\(\frac{1}{3}x+\frac{2}{5}\left(x-1\right)=0\)

\(\Leftrightarrow\frac{1}{3}x+\frac{2}{5}x-\frac{2}{5}=0\)

\(\Leftrightarrow\frac{1}{3}x+\frac{2}{5}x=0+\frac{2}{5}\)

\(\Leftrightarrow x\left(\frac{1}{3}+\frac{2}{5}\right)=\frac{2}{5}\)

\(\Leftrightarrow x\left(\frac{5}{15}+\frac{6}{15}\right)=\frac{2}{5}\)

\(\Leftrightarrow\frac{11}{15}x=\frac{2}{5}\)

\(\Leftrightarrow x=\frac{2}{5}\div\frac{11}{15}\)

\(\Leftrightarrow x=\frac{6}{11}\)

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{49}{50}\)

\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{49}{50}\)

\(\Leftrightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{49}{50}\)

\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{49}{50}\)

\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{49}{50}\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{49}{50}\div2\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{49}{50}\times\frac{1}{2}\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{49}{100}\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{49}{100}\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{50}{100}-\frac{49}{100}\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{100}\)

\(\Leftrightarrow x+1=100\)

\(\Leftrightarrow x=100-1\)

\(\Leftrightarrow x=99\)

\(\left(\frac{1}{3}+\frac{1}{6}\right).2^{x+4}-2^x=2^{13}-2^{10}\)

\(\frac{1}{2}.2^x.2^4-2^x=8192-1024\)

\(2^x.8-2^x=7168\)

\(2^x\left(8-1\right)=7168\)

\(2^x.7=7168\)

\(2^x=7168\div7\)

\(2^x=1024\)

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

\(\Rightarrow x=10\)

Vậy \(x=10\).

(1/3+1/6).2^x.2^4-2^x=8192-1024

(1/3+1/6).2^x.2^4-2^x=7168

1/2.2^x.2^4-2^x=7168

1/2.2^x.(2^4-1)=7168

1/2.2^x.(8-1)=7168

1/2.2^x.7=7168

1/2.2^x=7168:7

1/2.2^x=1024

      2^x=1024:1/2

     2^x=2048

2^x=2^11

x=11

vậy x=11