Question

x^2+9^log3(x)=8 ..... x=?

Answer 1

[tex]\text{Se foloseste identitatea}\ \boxed{a^{\log _b c}=c^{\log _b a}}.\\ x^2+9^{\log_3 x}=8\\ x^2+x^{\log_3 9}=8\\ x^2+x^2=8\\ 2x^2=8\\ x^2=4\\ x=2\\ \text{Obs: x nu poate fi -2 din cauza conditiei de existenta a logaritmului.}[/tex]