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========== 1 ==========
![2^x-1 \leq 0\\
2^x \leq 1\\
2^x \leq 2^0\\
2\ \textgreater \ 1 \Rightarrow \\
x \leq 0
2^x-1 \leq 0\\
2^x \leq 1\\
2^x \leq 2^0\\
2\ \textgreater \ 1 \Rightarrow \\
x \leq 0](https://tex.z-dn.net/?f=2%5Ex-1++%5Cleq+0%5C%5C%0A2%5Ex+%5Cleq+1%5C%5C%0A2%5Ex+%5Cleq+2%5E0%5C%5C%0A2%5C+%5Ctextgreater+%5C+1++%5CRightarrow+%5C%5C%0Ax+%5Cleq+0%0A)
========== 2 ==========
![log_{0.5}x^2-1 \geq 0\\
===============\\
x^2\ \textgreater \ 0\\
x\in R, x\neq0\\
===============\\
log_{0.5}x^2 \geq 1\\
log_{0.5}x^2 \geq log_{0.5}0.5\\
0\ \textless \ 0.5\ \textless \ 1 \Rightarrow \\
x^2 \leq 0.5\\
x^2-0.5 \leq 0\\
x^2- \frac{1}{2} \leq 0\\
(x- \frac{1}{ \sqrt{2} } )(x+ \frac{1}{ \sqrt{2} } ) \leq 0\\
x \in [- \frac{1}{ \sqrt{2} }; \frac{1}{ \sqrt{2} }]\\
===============\\
\left \{ {{x\in R, x\neq0} \atop {x \in [- \frac{1}{ \sqrt{2} }; \frac{1}{ \sqrt{2} }]} \right. \\\\
log_{0.5}x^2-1 \geq 0\\
===============\\
x^2\ \textgreater \ 0\\
x\in R, x\neq0\\
===============\\
log_{0.5}x^2 \geq 1\\
log_{0.5}x^2 \geq log_{0.5}0.5\\
0\ \textless \ 0.5\ \textless \ 1 \Rightarrow \\
x^2 \leq 0.5\\
x^2-0.5 \leq 0\\
x^2- \frac{1}{2} \leq 0\\
(x- \frac{1}{ \sqrt{2} } )(x+ \frac{1}{ \sqrt{2} } ) \leq 0\\
x \in [- \frac{1}{ \sqrt{2} }; \frac{1}{ \sqrt{2} }]\\
===============\\
\left \{ {{x\in R, x\neq0} \atop {x \in [- \frac{1}{ \sqrt{2} }; \frac{1}{ \sqrt{2} }]} \right. \\\\](https://tex.z-dn.net/?f=log_%7B0.5%7Dx%5E2-1+%5Cgeq+0%5C%5C%0A%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%5C%5C%0Ax%5E2%5C+%5Ctextgreater+%5C+0%5C%5C%0Ax%5Cin+R%2C+x%5Cneq0%5C%5C%0A%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%5C%5C%0Alog_%7B0.5%7Dx%5E2+%5Cgeq+1%5C%5C%0Alog_%7B0.5%7Dx%5E2+%5Cgeq+log_%7B0.5%7D0.5%5C%5C%0A0%5C+%5Ctextless+%5C+0.5%5C+%5Ctextless+%5C+1+%5CRightarrow+%5C%5C%0Ax%5E2+%5Cleq+0.5%5C%5C%0Ax%5E2-0.5++%5Cleq+0%5C%5C%0Ax%5E2-+%5Cfrac%7B1%7D%7B2%7D+++%5Cleq+0%5C%5C%0A%28x-+%5Cfrac%7B1%7D%7B+%5Csqrt%7B2%7D+%7D+%29%28x%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%7B2%7D+%7D+%29+%5Cleq+0%5C%5C%0Ax+%5Cin+%5B-+%5Cfrac%7B1%7D%7B+%5Csqrt%7B2%7D+%7D%3B+%5Cfrac%7B1%7D%7B+%5Csqrt%7B2%7D+%7D%5D%5C%5C%0A%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%5C%5C%0A+%5Cleft+%5C%7B+%7B%7Bx%5Cin+R%2C+x%5Cneq0%7D+%5Catop+%7Bx+%5Cin+%5B-+%5Cfrac%7B1%7D%7B+%5Csqrt%7B2%7D+%7D%3B+%5Cfrac%7B1%7D%7B+%5Csqrt%7B2%7D+%7D%5D%7D+%5Cright.+%5C%5C%5C%5C%0A)
![x\in [- \frac{1}{ \sqrt{2} }; 0)\cup(0;\frac{1}{ \sqrt{2} }] x\in [- \frac{1}{ \sqrt{2} }; 0)\cup(0;\frac{1}{ \sqrt{2} }]](https://tex.z-dn.net/?f=x%5Cin++%5B-+%5Cfrac%7B1%7D%7B+%5Csqrt%7B2%7D+%7D%3B+0%29%5Ccup%280%3B%5Cfrac%7B1%7D%7B+%5Csqrt%7B2%7D+%7D%5D)
========== 2 ==========
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