Question

log5 x * (log5 x - 1) = 2​

Answer 1

$\displaystyle\bf\\ODZ:\\\\x>0\\\\\\\log_{5} x\cdot(\log_{5} x-1)=2\\\\\\\log_{5} ^{2} x-\log_{5} x-2=0\\\\\\\log_{5} x=m\\\\\\m^{2} -m-2=0\\\\\\D=(-1)^{2} -4\cdot(-2)=1+8=9=3^{2} \\\\\\m_{1} =\frac{1-3}{2} =-1\\\\\\m_{2} =\frac{1+3}{2} =2\\\\\\1)\\\\\log_{5} x=-1\\\\\\x_{1} =5^{-1} =\frac{1}{5} =0,2\\\\\\2)\\\\\log_{5} x=2\\\\\\x_{2} =5^{2} =25\\\\\\Otvet:0,2 \ \ ; \ \ 25$