Question

The values of $x$ satisfying ${\log }_3(x^2+4x+12)=2$ are

• A. $2,-4$
• B. $1,-3$
• C. $-1,3$
• D. $-1,-3$

Answer 1

The correct option is D $-1,-3$

Point (4,-3)

ellipse $2x^2+5y^2=20$

by substituting the co-ordinates of the point in ellipse

$2(4{)}^2+5(-3{)}^2=20$

$\Rightarrow 32+45-20=0$

$\Rightarrow 57>0$

we get a the value that means point is outside the circle.

$\Rightarrow lo{g}_3(x^2+4x+12)=2$ if $lo{g}_a^b$= k $b=a^k$

$\Rightarrow x^2+4x+12=3^2$

$\Rightarrow x^2+4x+12-9=0$

$\Rightarrow x^2+4x+3=0$

$\Rightarrow x^2+3x+x+3=0$

$\Rightarrow (x+1)(x+3)=0$

x = -1 , -3