a. \(\Rightarrow\frac{1.2.3.4.5....30.31}{4.6.8.10.12....62.64}=2^x\)

\(\Rightarrow\frac{1.2.3.4.5....30.31}{2.2.3.2.4.2.5.2.6.2....31.2.64}=2^x\)

\(\Rightarrow\frac{1}{2.2.2.2....2.2\left(\text{30 số 2}\right).64}=2^x\)

\(\Rightarrow\frac{1}{2^{30}.2^6}=2^x\)

\(\Rightarrow\frac{1}{2^{36}}=2^x\)

\(\Rightarrow2^{-36}=2^x\)

Vậy \(x=-36\).

b.\(9^{2x-1}=\frac{1}{3}\)

\(\Rightarrow\left(3^2\right)^{2x-1}=\frac{1}{3}\)

\(\Rightarrow3^{2.\left(2x-1\right)}=\frac{1}{3}\)

\(\Rightarrow3^{4x-2}=\frac{1}{3}\)

\(\Rightarrow3^{4x-2}=3^{-1}\)

\(\Rightarrow4x-2=-1\)

=> 4x=-1+2

=> 4x=1

Vậy x =\(\frac{1}{4}\)

c.\(3.8^x-2.2^{3x}-16=0\)

\(\Rightarrow3.\left(2^3\right)^x-2.2^{3x}-16=0\)

\(\Rightarrow3.2^{3x}-2.2^{3x}-16=0\)

\(\Rightarrow2^{3x}.\left(3-2\right)-16=0\)

\(\Rightarrow2^{3x}.1-16=0\)

\(\Rightarrow2^{3x}=16\)

\(\Rightarrow2^{3x}=2^4\)

=> 3x=4

Vậy x=\(\frac{4}{3}\)

    \(\frac{3}{14}:\frac{1}{28}-\frac{13}{21}:\frac{1}{28}+\frac{29}{42}:\frac{1}{28}-8\)

\(=\left(\frac{3}{14}-\frac{13}{21}+\frac{29}{42}\right):\frac{1}{28}-8\)

\(=\left(\frac{9}{42}-\frac{26}{21}+\frac{29}{42}\right):\frac{1}{28}-8\)

\(=\left(\frac{-17}{42}+\frac{29}{42}\right):\frac{1}{28}-8\)

\(=\frac{12}{42}:\frac{1}{28}-8\)

\(=\frac{2}{7}.28-8\)

\(=\frac{56}{7}-8\)

\(=8-8\)

\(=0\)

D = -1-1/3-1/6-1/10-...-1/1225

Suy ra : D/2=-1/2-1/6-1/12-....-1/2450 
Mà 1/2=1/(1.2)=1-1/2; 1/6=1/(2.3)=1/2-1/3;...1/2450=1/(49.50)=... 
D/2= -(1-1/2)-(-1/2-1/3)-...-(1/49-1/50) 
D/2= -1+1/2-1/2+1/3-....-1/49+1/50 
D/2= -1+1/50=-49/50 
D=(-49/50).2=-98/50

k nha

a)Vì x^2 >=0 ; x^4>= 0 

=> A = x^4 + 3x^2 - 4 >= -4 

Vậy min A = -4 tại x  = 0 

b) x^2 >= 0 với mọi x 

=> B = ( x^2 + 5 )^2 + 4 >= ( 0 + 5 )^2 + 4 = 29 

Vậy Min B = 29 tại x = 0