Question

100 POINTS !! WILL MARK BRANILEST !! PLS HURRY

Answer 1

Answer:

$\sf x=2, \ x = -8$

solving steps:

$\hookrightarrow \sf log_4 x+log_4 (x+6)=2$

$\hookrightarrow \sf log_4 (x(x+6))=log_4 (16)$

$\hookrightarrow \sf log_4 (x^2+6x)=log_4 (16)$

$\hookrightarrow \sf x^2+6x=16$

$\hookrightarrow \sf x^2+6x-16=0$

$\hookrightarrow \sf x^2+8x-2x-16=0$

$\hookrightarrow \sf x(x+8)-2(x+8)=0$

$\hookrightarrow \sf (x-2)(x+8)=0$

$\hookrightarrow \sf x=2, \ x = -8$

Answer 2

Answer:

log4x+log4(x-6)=2

place under single log using multiplication rule

log4(x(x-6))=2

convert to exponential form:(base(4) raised to log of number(2)=number(x(x-6)

4^2=x(x-6)

16=x^2-6x

x^2-6x-16=0

(x-8)(x+2)=0

x=8

or

x=-2 (reject, x>0)

Step-by-step explanation: