از معادله $\frac{۱}{۲}{\log ^{۲۵}} + \log \left( {x - ۳} \right) = ۲$ عدد $x$ کدام است؟
$\frac{1}{2}{\log ^{25}} + {\log ^{\left( {x - 3} \right)}} = 2 \Rightarrow $${\log ^{{{\left( {{5^2}} \right)}^{\frac{1}{2}}}}} + {\log ^{\left( {x - 3} \right)}} = 2 \Rightarrow {\log ^5} + {\log ^{\left( {x - 3} \right)}} = 2$${\log ^{5\left( {x - 3} \right)}} = 2 \Rightarrow 5x - 15 = {10^2} \Rightarrow $$5x = 100 + 15 \Rightarrow 5x = 115 \Rightarrow x = \frac{{115}}{5} = 23$