Question

Розв’яжіть рівняння 0,5^5 – 2х + 3∙0,25^3 - х = 20

Answer 1

$0,5^{5-2x}+3\cdot 0,25^{3-x}=20\\\\(\frac{1}{2})^{5-2x}+3\cdot (\frac{1}{4})^{3-x}=20\\\\(\frac{1}{2})^{5-2x}+3\cdot (\frac{1}{2})^{6-2x}=20\\\\(\frac{1}{2})^{-2x}\cdot (\frac{1}{2^5}+3\cdot \frac{1}{2^6})=20\\\\2^{2x}\cdot \frac{2+3}{2^6}=20\\\\2^{2x}=\frac{20\cdot 2^6}{5}\\\\2^{2x}=4\cdot 2^6\\\\2^{2x}=2^2\cdot 2^6\\\\2^{2x}=2^8\\\\2x=8\\\\x=4$