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\(\left(\frac{9}{25}\right)^{-x}=\left(\frac{5}{3}\right)^{-6}\)
\(=>\left(\frac{3}{5}\right)^{-2x}=\left(\frac{5}{3}\right)^{-6}\)
\(=>\left(\frac{3}{5}\right)^{-2x}=\left(\frac{3}{5}\right)^6\)
\(=>-2x=6\)
\(=>x=-3\)
câu 2.
\(x^2-xy=-18\)
\(=>x\left(x-y\right)=-18\)
\(=>3x=-18\)
\(=>x=-6\)
\(\frac{2^{4-x}}{16^5}=32^6\)
=> \(\frac{2^{4-x}}{\left(2^4\right)^5}=\left(2^5\right)^6\)
=> \(\frac{2^{4-x}}{2^{20}}=2^{30}\)
=> \(2^{4-x}=2^{30}.2^{20}\)
=> \(2^{4-x}=2^{50}\)
=> 4 - x = 50
=> x = 4 - 50 = -46
\(\frac{3^{2x+3}}{9^3}=9^{14}\)
=> \(\frac{3^{2x+3}}{\left(3^2\right)^3}=\left(3^2\right)^{14}\)
=> \(\frac{3^{2x+3}}{3^6}=3^{28}\)
=> \(3^{2x+3}=3^{28}.3^6\)
=> \(3^{2x+3}=3^{34}\)
=> 2x + 3 = 34
=> 2x = 34 - 3
=> 2x = 31
=> x = 31/2
\(\left(\left(\frac{3}{4}\right)^3\right)^2=\left(\frac{9}{16}\right)^x\)
=>\(\left(\frac{3}{4}\right)^6=\left(\left(\frac{3}{4}\right)^2\right)^x\)
=>\(\left(\frac{3}{4}\right)^6=\left(\frac{3}{4}\right)^{2x}\)
=>6=2x
=>x=3
Sorry, cho mình làm lại:
\(\left(\left(\frac{3}{4}\right)^3\right)^2=\left(\frac{16}{9}\right)^x\)
=>\(\left(\frac{3}{4}\right)^6=\left(\left(\frac{4}{3}\right)^2\right)^x\)
=>\(\left(\frac{3}{4}\right)^6=\left(\frac{4}{3}\right)^{2x}\)
=>\(\left(\frac{3}{4}\right)^6=\frac{1}{\left(\frac{3}{4}\right)^{2x}}\)
=>\(\left(\frac{3}{4}\right)^6=\left(\frac{3}{4}\right)^{-2x}\)
=>6=-2x
=>-6=2x
=>x=-3
Xét trường hợp giống câu kia đi :
Gợi ý :
Th1 : \(\left|x-\frac{3}{4}\right|\ge0\)
Th2 \(\left|x-\frac{3}{4}\right|< 0\)
\(\left(\frac{9}{25}\right)^{-x}=\left(\frac{5}{3}\right)^{-6}\Leftrightarrow\left(\frac{9}{25}\right)^{-x}=\left(\frac{3}{5}\right)^6=\left(\frac{9}{25}\right)^3\Leftrightarrow-x=3\Leftrightarrow x=-3\)