Question

o conjunto solucação da equação 10^log(x^2-3x+2)=6^loga10? heeelllpppp :)

Answer 1

$10^{log_a(x^2+3x+2)}=6^{log_a10} \\ \\ Vamos\,\, aplicar\,log_{10}~ em~ambos~os~ lados ~da~express\~ao \\ \\ log_{10}(10^{log_a(x^2+3x+2)})=log_{10}(6^{log_a10}) \\ \\ Propriedade{:}\,\, log_mn^k=k.log_mn\\ \\ log_a(x^2+3x+2)}.log_{10}10=log_a10.log_{10}6 \\ \\ Propriedades{:}\,\, log_mn= \frac{log_zn}{log_zn} \,\,e\,\, log_{10}10 =1 \\ \\ log_a(x^2+3x+2)}= log_a10.\frac{log_a6}{log_a10} \\ \\ log_a(x^2+3x+2)}=log_a6 \\ \\ x^2+3x+2=6 \\ \\ x^2+3x-4=0$
$Resolvendo \,\, por\,\, Bhaskara \\ \\ \Delta=(3)^2-4.(1)(-4)=9+16=25 \\ \\ \sqrt{\Delta} =5 \\ \\ x_1= \frac{-(3)+5}{2(1)} =1 \\ \\ x_1= \frac{-(3)-5}{2(1)} =-4 \\ \\ S=\{1 ,-4\}$