2^(x-2)=5^(x^2-5x+6)решить уравнение, 11 класс

Решите задачу:

$\displaystyle 2^{x-2}=5^{x^2-5x+6}\\\\x^2-5x+6=(x-2)(x-3)\\\\2^{x-2}=5^{(x-2)(x-3)}\\\\(2^1)^{x-2}=(5^{x-3})^{x-2}\\\\a^x=b^x \to a=b\\\\a^x=b^x \to x=0\\\\ \left \ [ {{x-2=0} \atop {2=5^{x-3}}} \right.\\\\\left \ [ {{x=2} \atop {2=5^x*5^{-3}}}} \right.\\\\ \left \ [ {{x=2} \atop {5^x=250}}} \right.\\\\ \left \ [ {{x=2} \atop {5^x=5^3*2}}} \right.\\\\ \left \ [ {{x=2} \atop {x=3+Log_52}}} \right.\\$