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\(^{2^{3x+2}=4^{x+5}}\)
\(^{ }\Rightarrow\)\(2^{3x}.2^2=4^x.4^5\)
\(\Rightarrow\)\(2^{3x}:4^x=4^5:2^2\)
\(\Rightarrow\)\(^{2^{3x}:2^{2x}=2^{10}:2^2}\)
\(\Rightarrow\)\(^{2^x=2^8}\)
\(\Rightarrow\)x=8
Vậy x=8
\(2^{3x+2}=4^{x+5}\)
\(\Rightarrow\left(2^3\right)^x.2^2=4^x.4^5\)
\(\Rightarrow4^x.2^x.2^2=4^x.4^5\)
Chia hai vế cho 4x
\(\Rightarrow2^{x+2}=4^5\)
\(\Rightarrow2^{x+2}=2^{10}\)
\(\Rightarrow x+2=10\)
\(\Rightarrow x=8\)
\(3x+5=2.\left(x-\frac{1}{4}\right)\)
\(\Rightarrow3x+5=2.x-2.\frac{1}{4}\)
\(\Rightarrow3x+5=2x-\frac{1}{2}\)
\(\Rightarrow5+\frac{1}{2}=2x-3x\)
\(\Rightarrow\frac{11}{2}=-x\)
\(\Rightarrow x=-\frac{11}{2}\)
\(3x+5=2\left(x-\frac{1}{4}\right)\)
\(3x+5=2x-\frac{1}{2}\)
\(\Leftrightarrow3x-2x=-\frac{1}{2}-5\)
\(\Leftrightarrow x=-\frac{11}{2}\)
Vậy x = -11/2
a) \(\left(\frac{3}{5}x-\frac{2}{3}x-x\right).\frac{1}{7}=\frac{-5}{21}\)
\(\Rightarrow\left(\frac{3}{5}-\frac{2}{3}-1\right).x=\frac{-5}{21}:\frac{1}{7}=\frac{-5}{3}\)
\(\Rightarrow\frac{-16}{15}.x=\frac{-5}{3}\Rightarrow x=\frac{-5}{3}:\frac{-16}{15}=\frac{25}{16}\)
b) \(\left(x-\frac{1}{4}\right)^2=\frac{1}{36}\)
\(\Rightarrow\left(x-\frac{1}{4}\right)^2=\left(±\frac{1}{6}\right)^2\)
\(\Rightarrow\orbr{\begin{cases}x-\frac{1}{4}=\frac{1}{6}\\x-\frac{1}{4}=\frac{-1}{6}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{5}{12}\\x=\frac{1}{12}\end{cases}}\)