Question

Помогите пожалуйста, срочно 50 баллов

Answer 1

$a)\; \; logx=2log5-3log2+4loga\; \; ,\; \; a>0\\\\logx=log5^2-log2^3+loga^4\\\\logx=log\frac{5^2\cdot a^4}{2^3}\; \; ,\; \; \; logx=log\frac{25a^4}{8}\\\\x=\frac{25a^4}{8}\\\\\\b)\; \; logx=\frac{3loga-2logc+4logx}{6}\\\\6\, logx=loga^3-logc^2+logx^4\\\\logx^6=log\frac{a^3\cdot x^4}{c^2}\; \; ,\; \; x^6=\frac{a^3\cdot x^4}{c^2}\; \; ,\; \; \; \frac{x^6}{x^4}=\frac{a^3}{c^2}\\\\x^{2}=\frac{a^3}{c^2}\; \; ,\; \; x=\frac{\sqrt{a^3}}{c}\\\\\\c)\; \; logx=\frac{6}{7}\cdot (log(a-b)+2logb-3logc+\frac{1}{2}\, loga)$

$logx=\frac{6}{7}\cdot (log(a-b)+logb^2-logc^3+log\sqrt{a})\\\\logx=\frac{6}{7}\cdot log\frac{(a-b)\cdot b^2\cdot \sqrt{a}}{c^3}\\\\logx=log\Big (\frac{(a-b)\cdot b^2\cdot \sqrt{a}}{c^3}\Big )^{\frac{6}{7}}\\\\x=\frac{\sqrt[7]{(a-b)^6}\cdot \sqrt[7]{b^{12}}\cdot \sqrt[14]{a^6}}{\sqrt[7]{c^{18}}}$