Question

Егэ профильная №17. как решить уравнение

Answer 1

$1,01^x \cdot 8 - 1,01^{x - 1} = 1 \\ \\ 8,08 \cdot 1,01^{x - 1} - 1,01^{x - 1} = 1 \\ \\ 1,01^{x - 1}(8,08 - 1) = 1 \\ \\ 1,01^ {x - 1} \cdot 7,08 = 1 \\ \\ 1,01^{x - 1} = \dfrac{1}{7,08} \\ \\ 1,01^{x - 1} = \dfrac{25}{177} \\ \\ \bigg ( \dfrac{101}{100} \bigg )^{x - 1} = \dfrac{25}{177} \\ \\ \\ x - 1 = log_{\dfrac{25}{177}}\dfrac{101}{100} \\ \\ \\ x = log_{\dfrac{25}{177}}\dfrac{101}{100} + 1$

$x = log_{\dfrac{25}{177}}\dfrac{101}{100} + 1 \\ \\ x = log_{\dfrac{25}{177}}\dfrac{101}{100} + log_{\dfrac{25}{177}} \dfrac{25}{177}} \\ \\ \\ x = log_{\dfrac{25}{177}} \dfrac{101 \cdot 25}{177 \cdot 100} \\ \\ x = log_{\dfrac{25}{177}} \dfrac{101 }{708}$