Question

2^(x-2)=5^(x^2-5x+6)

решить уравнение, 11 класс

Answer 1

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