Question

розв'яжи логарифмічне рівняння

Answer 1

$\displaystyle\bf\\ODZ:x > 0\\\\\log_{5} ^{2} x-9=0\\\\\log_{5} ^{2} x=9\\\\\\\left[\begin{array}{ccc}\log_{5} x=3\\\log_{5} x=-3\end{array}\right\\\\\\\left[\begin{array}{ccc}x_{1}=5^{3} \\x_{2} =5^{-3} \end{array}\right\\\\\\\left[\begin{array}{ccc}x_{1} =125\\x_{2} =\frac{1}{125} \end{array}\right\\\\\\Otvet \ : \ x_{1} =125 \ \ ; \ \ x_{2} =\frac{1}{125}$