[tex]6^{4x+1}=5^{x-3}\\\\\log6^{4x+1}=\log5^{x-3}\\\\(4x+1)\log 6=(x-3)\log 5\\\\(4x+1)\log 6-(x-3)\log 5=0\\\\4x\log 6+\log 6-x\log 5+3\log 5=0\\\\4x\log 6-x\log 5 = -3\log 5-\log 6\\\\x(4\log 6-\log 5) = -3\log 5-\log 6\\\\x=\dfrac{-3\log 5-\log 6}{4\log 6-\log 5}\\\\x=\dfrac{3\log 5+\log 6}{\log 5-4\log 6}[/tex]
