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=\(\frac{4}{3}\)