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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\(\Leftrightarrow x+1=100\)

\(\Leftrightarrow x=100-1\)

\(\Leftrightarrow x=99\)

2^x+2.2^x=40

=>2^x.2².2^x=40

=>2^x.2^x..4=40

=>2^x.2^x=40:4

=>2^x.2^x=10

=>x không tồn tại

\(2^{x+2}.2^x=40\)

\(2^x.2^2.2^x=40\)

\(2^x.2^x=40:2^2\)

\(2^x.2^x=10\)

=> x không tồn tại

\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+.......+\dfrac{1}{x\left(x+1\right)}=\dfrac{44}{45}\)

=> \(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}+......+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{44}{45}\)

=> \(1-\dfrac{1}{x+1}=\dfrac{44}{45}\)

=> \(\dfrac{x+1}{x+1}-\dfrac{1}{x+1}=\dfrac{44}{45}\)

=> \(\dfrac{x+1-1}{x+1}=\dfrac{44}{45}\)

=> \(\dfrac{x}{x+1}=\dfrac{44}{45}\)

=> 44(x+1)=45x

=> 44x+44=45x

=> 44x-45x=-44

=> -1x=-44

=> x=44

vậy x=44

dễ thì tự giải đi

a)x=11

b) x=1

c) x=2

d) x=15

e) x=3

g) x=15

1, Ta có :

a . 81 = 3⁴ => 3^x= 3⁴ => x = 4 .

b. 125 = 5³ => 5^x+2 = 5³ =>x + 2 = 3 => x = 1

c. 2³ * 2^{x - 1} = 64

=> 2^{3 + ( x - 1 )} = 64 = 2⁶ 

^{=>  3 + ( x - 1 ) = 6} 

^{=>           x - 1   = 6 - 3 = 3}

                      ^{x  = 3 + 1}

                       ^{x  = 4}

3/ \(2\left(x-3\right)-3\left(1-2x\right)=4+4\left(1-x\right)\)

\(\Leftrightarrow2x-6-3+6x=4+4-4x\)

\(\Leftrightarrow8x-9=8-4x\)

\(\Leftrightarrow8x+4x=8+9\)

\(\Leftrightarrow12x=17\)

\(\Leftrightarrow x=\dfrac{17}{12}\)

Vậy \(x=\dfrac{17}{12}\)

4/ \(\dfrac{x-2}{2}-\dfrac{1+x}{3}=\dfrac{4-3x}{4}-1\)

\(\Leftrightarrow6\left(x-2\right)-4\left(1+x\right)=3\left(4-3x\right)-12\)

\(\Leftrightarrow6x-12-4-4x=12-9x-12\)

\(\Leftrightarrow6x-4-4x=12-9x\)

\(\Leftrightarrow2x-4=12-9x\)

\(\Leftrightarrow2x+9x=12+4\)

\(\Leftrightarrow11x=16\)

\(\Leftrightarrow x=\dfrac{16}{11}\)

Vậy \(x=\dfrac{16}{11}\)