a.15-(5-2x)=-4

\(\Leftrightarrow\)15-5+2x=-4

\(\Leftrightarrow\)2x=-4-15+5

\(\Leftrightarrow\)2x=-14

\(\Leftrightarrow\)x=-7

b.TH1:x-3\(\ge\)0 \(\Rightarrow\)x\(\ge\)3

Ta có \(|\)x-3\(|\)=x-3

PT trên\(\Leftrightarrow\)x-3+1=4

             \(\Leftrightarrow\)x=4+3-1

            \(\Leftrightarrow\)x=6(nhận)

TH2:x-3<0\(\Leftrightarrow\)x<3

Ta có:\(|\)x-3\(|\)=-x+3

PT trên\(\Leftrightarrow\)-x+3+1=4

                       -x=4-3-1

                       x=0(nhận)

Vậy S={0;6}

chỗ 100000 là 1000000000000000000.mười tám chữ số 0

a) \(5^{x+1}-2.5^x=375\)
\(\Rightarrow5^x\left(5-2\right)=375\)
\(\Rightarrow5^x.3=375\)
\(\Rightarrow5^x=125=5^3\)
\(\Rightarrow x=3\)
b) \(9^{x+1}-5.3^{2x}=324\)
\(\Rightarrow3^{2\left(x+1\right)}-5.3^{2x}=324\)
\(\Rightarrow3^2\left(3^{x+1}-5.3^x\right)=324\)
\(\Rightarrow9.3^x\left(3-5\right)=324\)
\(\Rightarrow3^x.\left(-2\right)=36\)
\(\Rightarrow3^x=-18=3^2.\left(-2\right)\)(vô lí vì 3^x không chia hết cho 2)
c) \(\left(1-x\right)^5=32=2^5\)
\(\Rightarrow1-x=2\)
\(\Rightarrow x=-1\)
d) \(3.5^{2x+1}-3.25^x=300\)
\(\Rightarrow3\left(5^{2x}.5-5^{2x}\right)=300\)
\(\Rightarrow5^{2x}\left(5-1\right)=100\)
\(\Rightarrow5^{2x}.4=100\)
\(\Rightarrow5^{2x}=25=5^2\)
\(\Rightarrow2x=2\)
\(\Rightarrow x=1\)
 

a) \(2^x+5=21\)

\(\Rightarrow2^x=21-5=16\Rightarrow2^x=2^4\)

Vậy x  = 4

b) \(2^x-1+3^2=5^2+2.5\)

\(\Rightarrow2^x-1+9=35\)

\(\Rightarrow2^x=35-9+1=27\)

Vậy x không có giá trị

c;d;e;f làm tương tự

Ta có: \(\left(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{13\cdot15}\right)\cdot\left(x-1\right)=\frac{3}{5}x-\frac{7}{15}\)

\(\Leftrightarrow\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\right)\cdot\left(x-1\right)=\frac{3x}{5}-\frac{7}{15}\)

\(\Leftrightarrow\frac{14}{15}\cdot\left(x-1\right)=\frac{9x-7}{15}\)

\(\Leftrightarrow x-1=\frac{9x-7}{15}:\frac{14}{15}=\frac{9x-7}{14}\)

hay \(x=\frac{9x-7}{14}+1=\frac{9x-7}{14}+\frac{14}{14}=\frac{9x+7}{14}\)

\(\Leftrightarrow x\cdot14=9x+7\)

\(\Leftrightarrow14x-9x-7=0\)

\(\Leftrightarrow5x-7=0\)

\(\Leftrightarrow5x=7\)

hay \(x=\frac{7}{5}\)

Vậy: \(x=\frac{7}{5}\)

a: =>31-x=60

=>x=-29

b: =>(x-140):35=280-270=10

=>x-140=350

=>x=490

c: =>(1900-2x):35=48

=>1900-2x=1680

=>2x=220

=>x=110

d: =>\(2^{2x-1}=2^9\cdot2=2^{11}\)

=>2x-1=11

=>x=6

e: =>(x+2)^5=4^5

=>x+2=4

=>x=2

f: =>3x-4=0 hoặc x-1=0

=>x=4/3 hoặc x=1

g: =>(2x-1)^2=49

=>2x-1=7 hoặc 2x-1=-7

=>x=-3 hoặc x=4

h: =>x(x+1)/2=78

=>x(x+1)=156

=>x=12

a: \(=\dfrac{2^{13}\cdot5^7\left(2^{17}+5^{20}\right)}{2^{10}\cdot5^7\left(2^{17}+5^{20}\right)}=2^3\)

b: \(M=\left(7-4\right)^{\left(7-5\right)^{\left(7-6\right)^{\left(7+6\right)^{\left(7+5\right)}}}}\)

\(=3^{2\cdot1\cdot13\cdot12}=3^{312}\)

Ta có : \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{x\left(x+2\right)}=\frac{16}{34}\)

=> \(2\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{x\left(x+2\right)}\right)=2.\frac{16}{34}\)

=> \(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{x\left(x+2\right)}=\frac{16}{17}\)

=> \(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}=\frac{16}{17}\)

=> \(1-\frac{1}{x+2}=\frac{16}{17}\)

=> \(\frac{1}{x+2}=1-\frac{16}{17}=\frac{1}{17}\)

=> \(x+2=17\)

=> \(x=15\)

=>1/1-1/3+1/3-1/5+1/5-1/7+....+1/x-1/(x+2)=16/34

=>1/1-1/(x+2)=16/34

=>1/(x+2)=1-16/34

=>1/(x+2)=9/17

=>(x+2).9=17

=>(x+2)=17/9

=>x=17/9-2

=>x=-1/9(không là số tự nhiên)

vậy không có số tự nhiên x thoả mãn điều kiện bài toán 

ôi mình làm sai rồi 

 m , Ta có : \(\left(1900-2.x\right):3-32=16\)

 \(\Leftrightarrow\frac{1900-2.x}{35}-32=16\)( Nhân hai vế với 35 ) 

 \(\Leftrightarrow1900-2.x-1120=560\)

  \(\Leftrightarrow780-2.x=560\)

 \(\Leftrightarrow-2.x=560-780\)

\(\Leftrightarrow\) \(-2.x=-220\)

 \(\Rightarrow x=110\)

Vậy x = 110

n, Ta có : \(720:\left[41-\left(2.x-5\right)\right]=2^3.5\)

             \(\Leftrightarrow720:\left(41-2.x+5\right)=8.5\)

              \(\Leftrightarrow720:\left(46-2.x\right)=40\)

              \(\Leftrightarrow\frac{720}{46-2.x}=40\)

              \(\Leftrightarrow\frac{720}{2.\left(23-x\right)}=40\)

               \(\Leftrightarrow\frac{360}{23-x}\)

               \(\Leftrightarrow360=40.\left(23-x\right)\)

               \(\Leftrightarrow9=23-x\)

               \(\Leftrightarrow x=14\)

Vậy x = 14

o, Ta có : \(\left(x-5\right).\left(x^2-4\right)=0\)

             \(\Leftrightarrow\orbr{\begin{cases}x-5=0\\x^2-4=0\end{cases}}\)

              \(\Rightarrow\orbr{\begin{cases}x=5\\x=\pm2\end{cases}}\)

Vậy \(x=5;-2;2\)