Question

Solve the equation. Check for extraneous solutions.
log base of 4 (x+6) + log base of 4(x)= 2
do the logs base of 4 cancel out??

Answer 1

log_4 (x + 6) + log_4 (x) = 2
Log properties.
log_4 [x(x + 6)] = 2
4 to the power of both sides
x² + 6x = 4^2
x² + 6x - 16 = 0
(x + 8)(x - 2) = 0
x = -8, 2

No real solutions to logarithms of neg numbers, so x = 2.