Question

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

Answer 1

$5times(sqrt[x]{64})=625\5sqrt[x]{64}=625\sqrt[x]{64}=125\64^{frac{1}{x}}=125,xneq0\frac{1}{x}=frac{1}{2}log_{2}(5)\2=log_{2}(5)x\x=frac{2}{log_{2}(5)},xneq0\x=frac{2}{log_{2}(5)}$

$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=-5times(-1)\x=5$