Question

8^(2-5x)=5^(5x-8)
Помогииииите!!!!

Answer 1

$8^{2-5x}=5^{5x-8}\\8^2cdot 8^{-5x}=5^{5x}cdot 5^{-8}\\frac{8^2}{8^{5x}}=frac{5^{5x}}{5^8}\\8^2cdot 5^8=5^{5x}cdot 8^{5x}\\8^2cdot 5^8=(5cdot 8)^{5x}\\40^{5x}=40^2cdot 5^6\\5x=log_{40}(40^2cdot 5^6)\\5x=log_{40}40^2+log_{40}5^6$

$5x=2+6cdot log_{40}5=2+6cdot frac{1}{log_540}=2+6cdot frac{1}{log_5(5cdot 8)}=2+6cdot frac{1}{1+3log_52}\\x=frac{2}{5}+frac{6}{5cdot (1+3log_52)}$