Question

Me podrian ayudar ??. Muchas Gracias : Ecuaciones Logaritmicas simples.

Answer 1

1.)

${log_4(x-6)=3}\\{log_4(x-6)=log_4(64)}\\{x-6=64}\\{x=6+64}\\{x=70}$

2.)

${log_6(x^2-2)=2}\\{log_6(x^2-2)=log_6(36)}\\{x^2-2=36}\\{x^2=36+2}\\{x^2=38}\\{x= \sqrt{38} }$


3.)

${log_3(x^2+x+3)=2}\\{log_3(x^2+x+3)=log_3(9)}\\{x^2+x+3=9}\\{x^2+x-6=0}\\{(x+3)(x-2)=0}\\\\{x-2=0 }\\{x=2}\\\\{x+3=0}\\{x=-3}$


4.)

${log_2(x^2-x+14)=4}\\{log_2(x^2-x+14)=log_2(16)}\\{x^2-x+14=16}\\{x^2-x-2=0}\\{(x-2)(x+1)=0}\\\\{x-2=0 }\\{x=2}\\\\{x+1=0}\\{x=-1}$


5.)

${log_3(x^2+x+15)=3}\\{log_3(x^2+x+15)=log_3(27)}\\{x^2+x+15=27}\\{x^2+x-12=0}\\{(x+4)(x-3)=0}\\\\{x+4=0 }\\{x=-4}\\\\{x-3=0}\\{x=3}$


Salu2. :)