Question

What are the potential solutions of log4X+log4(x+6)=2?

Answer 1

Answer:

Ox=-2 and x=-8

Step-by-step explanation:

Answer 2

Answer:

x = 2 ;   x = -8

Step-by-step explanation:

Log rule: Log a + log b = log a*b

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

    log₄  ( x² + 6x) = 2

                        4² = x² + 6x

         x² + 6x - 16 = 0

   x² - 2x + 8x - 16 = 0  

   x(x - 2) + 8(x - 2) = 0

       (x - 2) (x + 8)   = 0

x - 2 = 0  or x + 8 = 0

    x  = 2  or      x  = - 8