Question

Log0.6(x-5)=-2 помогите срочно!!!!

Answer 1

$log_{0,6}(x-5)=-2\\x-5\ \textgreater \ 0\\x\ \textgreater \ 5\\\\log_{0,6}(x-5)=log_{0,6}(0,6^{-2})\\\\x-5=( \frac{6}{10})^{-2}\\\\x-5=( \frac{10}{6})^2\\\\x-5=( \frac{5}{3})^2\\\\x-5= \frac{25}{9}\\\\x=5+ \frac{25}{9}\\\\x=5+2 \frac{7}{9}\\\\x=7 \frac{7}{9} \in(5;+\infty)$

Answer 2

$log_{0,6}(x-5)=-2$

Используем основное свойства логарифма

${0,6}^{-2} = (x-5)$

$( \frac{5}{3}) ^{2} = (x-5)$

$\frac{25}{9} = (x-5)$

$25 = 9x-45$

$9x = 70$

$x = \frac{70}{9} = 7 \frac{7}{9}$