Question

What are the solutions to
log3x + log3(x2 + 2) = 1 + 2log3x?

Answer 1

Hi,

Explanation:

`log_3(x)+log_3(x^2+2)=1+2*log_3(x)\\\\log_3(x^2+2)-log_3(x)=1\\\\log_3((x^2+2)/(x)) =1\\\\(x^2+2)/(x)=3^1\\\\x^2-3x+2=0\\\\x^2-x-2x+2=0\\\\x(x-1)-2(x-1)=0\\\\(x-1)(x-2)=0\\\\\boxed{x=1\ or\ x=2}\\`