![2^{x+5}\leq (\frac{1}{4})^{2x-3}
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2^{x+5}\leq (2^{-2})^{2x-3}
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2^{x+5} \leq 2^{-4x+6}
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x+5 \leq -4x+6
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5x \leq 1
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x \leq 0.2](https://tex.z-dn.net/?f=2%5E%7Bx%2B5%7D%5Cleq+%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7B2x-3%7D%0A%5C%5C%5C%0A2%5E%7Bx%2B5%7D%5Cleq+%282%5E%7B-2%7D%29%5E%7B2x-3%7D%0A%5C%5C%5C%0A2%5E%7Bx%2B5%7D+%5Cleq+2%5E%7B-4x%2B6%7D%0A%5C%5C%5C%0Ax%2B5+%5Cleq+-4x%2B6%0A%5C%5C%5C%0A5x+%5Cleq+1%0A%5C%5C%5C%0Ax+%5Cleq+0.2 "2^{x+5}\leq (\frac{1}{4})^{2x-3}
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2^{x+5}\leq (2^{-2})^{2x-3}
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2^{x+5} \leq 2^{-4x+6}
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x+5 \leq -4x+6
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5x \leq 1
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x \leq 0.2")
![0.7^x \geq 0.49^{5-x}
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0.7^x \geq 0.7^{10-2x}
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x \leq 10-2x
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3x \leq 10
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x \leq \frac{10}{3}](https://tex.z-dn.net/?f=0.7%5Ex+%5Cgeq+0.49%5E%7B5-x%7D%0A%5C%5C%5C%0A0.7%5Ex+%5Cgeq+0.7%5E%7B10-2x%7D%0A%5C%5C%5C%0Ax+%5Cleq+10-2x%0A%5C%5C%5C%0A3x+%5Cleq+10%0A%5C%5C%5C%0Ax+%5Cleq++%5Cfrac%7B10%7D%7B3%7D+ "0.7^x \geq 0.49^{5-x}
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0.7^x \geq 0.7^{10-2x}
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x \leq 10-2x
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3x \leq 10
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x \leq \frac{10}{3}")
64^{x^2-4}
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(2^{-2} )^{3x}>(2^6)^{x^2-4}
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2^{-6x}>2^{6x^2-24}
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-6x>6x^2-24
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6x^2+6x-24<0
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x^2+x-4<0
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D=1+4\cdot4=17
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x= \frac{-1\pm \sqrt{17} }{2}
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x\in(\frac{-1-\sqrt{17} }{2} ; \frac{-1+\sqrt{17} }{2} )" alt="( \frac{1}{4} )^{3x}>64^{x^2-4}
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(2^{-2} )^{3x}>(2^6)^{x^2-4}
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2^{-6x}>2^{6x^2-24}
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-6x>6x^2-24
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6x^2+6x-24<0
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x^2+x-4<0
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D=1+4\cdot4=17
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x= \frac{-1\pm \sqrt{17} }{2}
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x\in(\frac{-1-\sqrt{17} }{2} ; \frac{-1+\sqrt{17} }{2} )" align="absmiddle" class="latex-formula">
0}} \right. \\\ 0 0}} \right. \\\ 0
( \frac{3}{4})^{-2} } \atop {4x+3>0}} \right.
\\\
\left \{ {{4x+3> \frac{16}{9} } \atop {x>- \frac{4}{3} }} \right.
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\left \{ {{4x>- \frac{11}{9} } \atop {x>- \frac{4}{3} }} \right.
\\\
\left \{ {{x>- \frac{11}{36} } \atop {x>- \frac{4}{3} }} \right.
\\\
x>- \frac{11}{36}" alt="\log_{ \frac{3}{4} }(4x+3)<-2
\\\
\left \{ {{4x+3>( \frac{3}{4})^{-2} } \atop {4x+3>0}} \right.
\\\
\left \{ {{4x+3> \frac{16}{9} } \atop {x>- \frac{4}{3} }} \right.
\\\
\left \{ {{4x>- \frac{11}{9} } \atop {x>- \frac{4}{3} }} \right.
\\\
\left \{ {{x>- \frac{11}{36} } \atop {x>- \frac{4}{3} }} \right.
\\\
x>- \frac{11}{36}" align="absmiddle" class="latex-formula">
0}} \right. \\\ \left \{ {{-x \leq 8} \atop {x> 9}} \right. \\\ \left \{ {{x \geq -8} \atop {x >9}} \right. \\\ x >9" alt="\lg(x-9) \leq \lg(2x-1) \\\ \left \{ {{x-9 \leq 2x-1} \atop {x-9 >0}} \right. \\\ \left \{ {{-x \leq 8} \atop {x> 9}} \right. \\\ \left \{ {{x \geq -8} \atop {x >9}} \right. \\\ x >9" align="absmiddle" class="latex-formula">
2
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3x+1>7^2
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3x+1>49
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3x>48
\\\
x>12" alt="\log_7(3x+1)>2
\\\
3x+1>7^2
\\\
3x+1>49
\\\
3x>48
\\\
x>12" align="absmiddle" class="latex-formula">
0}} \right. \\\ \left \{ {{2x \leq8} \atop {x> \frac{7}{3} }} \right. \\\ \left \{ {{x \leq4} \atop {x> \frac{7}{3} }} \right. \\\ \frac{7}{3} 0}} \right. \\\ \left \{ {{2x \leq8} \atop {x> \frac{7}{3} }} \right. \\\ \left \{ {{x \leq4} \atop {x> \frac{7}{3} }} \right. \\\ \frac{7}{3}
\log_{0.5}(3-2x) \\\ \left \{ {{x<3-2x} \atop {x>0}} \right. \\\ \left \{ {{3x<3} \atop {x>0}} \right. \\\ \left \{ {{x<1} \atop {x>0}} \right. \\\ 0\log_{0.5}(3-2x) \\\ \left \{ {{x<3-2x} \atop {x>0}} \right. \\\ \left \{ {{3x<3} \atop {x>0}} \right. \\\ \left \{ {{x<1} \atop {x>0}} \right. \\\ 0