Question

log0,64(3x-50)=log1,25 0,5

Answer 1

ОДЗ : 3x - 50 > 0     ⇒   3x > 50    ⇒    x > 16 2/3

$log_{0,64}(3x-50)=log_{1,25}0,5\\\\log_{(\frac{4}{5})^{2}}(3x-50)=log_{(\frac{4}{5})^{-1}}0,5\\\\log_{\frac{4}{5} }(3x-50)^{\frac{1}{2}}=log_{\frac{4}{5} }(\frac{1}{2})^{-1}\\\\\sqrt{3x-50}=2\\\\(\sqrt{3x-50})^{2}=2^{2}\\\\3x-50=4\\\\3x=54\\\\x=18$