Question

Решить уравнения:
$5 \times ( \sqrt[x]{64} ) = 625$
${8}^{5 - x} = {7}^{x - 5}$

Answer 1

$5\times(\sqrt[x]{64})=625\\5\sqrt[x]{64}=625\\\sqrt[x]{64}=125\\64^{\frac{1}{x}}=125,x\neq0\\\frac{1}{x}=\frac{1}{2}log_{2}(5)\\2=log_{2}(5)x\\x=\frac{2}{log_{2}(5)},x\neq0\\x=\frac{2}{log_{2}(5)}$

$8^{5-x}=7^{x-5}\\5-x=\frac{log_{2}(7)x-5log_{2}(7)}{3}\\15-3x=log_{2}(7)x-5log_{2}(7)\\-3x-log_{2}(7)x=-5log_{2}(7)-15\\(-3-log_{2}(7))x=-5log_{2}(7)-15\\x=\frac{-5log_{2}(7)-15}{-3-log_{2}(7)}\\x=\frac{-5(log_{2}(7)+3)}{-(log_{2}(7)+3)}\\x=-5\times(-1)\\x=5$