0\\\\5^{log_5^2x}=5^{log_5x\cdot log_5x}=\Big (5^{log_5x}\Big )^{log_5x}=x^{log_5x}\; \; ,\; \; \; \Big [\; a^{log_{a}b}=b\, \Big ]\\\\x^{log_5x}+x^{log_5x}\geq 2\sqrt[4]5\\\\2x^{log_5x}\geq 2\sqrt[4]5\\\\x^{log_5x}\geq \sqrt[4]5\\\\log_5(x^{log_5x})\geq log_5\sqrt[4]5\\\\log_5x\cdot log_5x\geq \frac{1}{4}\cdot log_55\; \; \; \; \Big [\, log_{a}x^{k}=k\cdot log_{a}x\, \Big ]\\\\log_5^2x\geq \frac{1}{4}\\\\log_5^2x-\frac{1}{4}\geq 0" alt="5^{log_5^2x}+x^{log_5x}\geq 2\sqrt[4]5\; \; ,\; \; \; \; ODZ:\; x>0\\\\5^{log_5^2x}=5^{log_5x\cdot log_5x}=\Big (5^{log_5x}\Big )^{log_5x}=x^{log_5x}\; \; ,\; \; \; \Big [\; a^{log_{a}b}=b\, \Big ]\\\\x^{log_5x}+x^{log_5x}\geq 2\sqrt[4]5\\\\2x^{log_5x}\geq 2\sqrt[4]5\\\\x^{log_5x}\geq \sqrt[4]5\\\\log_5(x^{log_5x})\geq log_5\sqrt[4]5\\\\log_5x\cdot log_5x\geq \frac{1}{4}\cdot log_55\; \; \; \; \Big [\, log_{a}x^{k}=k\cdot log_{a}x\, \Big ]\\\\log_5^2x\geq \frac{1}{4}\\\\log_5^2x-\frac{1}{4}\geq 0" align="absmiddle" class="latex-formula">
![znaki:\qquad +++(-\frac{1}{2})---(\frac{1}{2})+++\\\\log_5x\leq -\frac{1}{2}\qquad ili\qquad log_5x\geq \frac{1}{2}\\\\0<x\leq 5^{-\frac{1}{2}}\qquad ili\qquad x\geq 5^{\frac{1}{2}}\\\\0<x\leq \frac{1}{\sqrt5}\qquad ili\qquad x\geq \sqrt5\\\\Otvet:\; \; x\in (0,\frac{1}{\srqt5}\, ]\cup [\, \sqrt5,+\infty )](https://tex.z-dn.net/?f=znaki%3A%5Cqquad%20%2B%2B%2B%28-%5Cfrac%7B1%7D%7B2%7D%29---%28%5Cfrac%7B1%7D%7B2%7D%29%2B%2B%2B%5C%5C%5C%5Clog_5x%5Cleq%20-%5Cfrac%7B1%7D%7B2%7D%5Cqquad%20ili%5Cqquad%20log_5x%5Cgeq%20%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C0%3Cx%5Cleq%205%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%5Cqquad%20ili%5Cqquad%20x%5Cgeq%205%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5C%5C%5C%5C0%3Cx%5Cleq%20%5Cfrac%7B1%7D%7B%5Csqrt5%7D%5Cqquad%20ili%5Cqquad%20x%5Cgeq%20%5Csqrt5%5C%5C%5C%5COtvet%3A%5C%3B%20%5C%3B%20x%5Cin%20%280%2C%5Cfrac%7B1%7D%7B%5Csrqt5%7D%5C%2C%20%5D%5Ccup%20%5B%5C%2C%20%5Csqrt5%2C%2B%5Cinfty%20%29 "znaki:\qquad +++(-\frac{1}{2})---(\frac{1}{2})+++\\\\log_5x\leq -\frac{1}{2}\qquad ili\qquad log_5x\geq \frac{1}{2}\\\\0<x\leq 5^{-\frac{1}{2}}\qquad ili\qquad x\geq 5^{\frac{1}{2}}\\\\0<x\leq \frac{1}{\sqrt5}\qquad ili\qquad x\geq \sqrt5\\\\Otvet:\; \; x\in (0,\frac{1}{\srqt5}\, ]\cup [\, \sqrt5,+\infty )")