Question

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

Ox=-2 and x=-8
Ox=-2 and x = 8
O x=2 and x=-8
Ox=2 and x=8

Answer 1

x = 2 ; x = -8

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