Question

5^x-5^(x-1)=100Как решать?

Answer 1

$5^x-5^{x-1}=100$

$5^x-5^x*5^{-1}=100$

$5^x(1-5^{-1})=100$

$5^x(1- \frac{1}{5})=100$

$5^x* \frac{4}{5}=100$

$5^x=100: \frac{4}{5}$

$5^x=100* \frac{5}{4}$

$5^x=125$

$5^x=5^3$

$x=3$

Проверка

$5^3-5^{3-1}=100$

$5^3-5^2=100$

$125-25=100$

$100=100$