log6 (x plus 5) plus log6 x equals 2

Question

log6 (x+5) + log6 x = 2

Answer 1

log6 (x+5) + log6 x = 2

log6((x( x + 5)) = 2

x( x + 5) = 6^2

x^2 + 5x = 36

x^2 + 4x - 36 = 0

( x - 4)(x + 9 ) = 0

x - 4 = 0 or x + 9 = 0

x =  4 or x = - 9

Answer 2

addition for logarithms is equivalent to multiplication so...

log6(x+5)(x) = 2, then using the definition of logarithms, change it to 6^2 = (x+5)(x) and solve

36= x^2 + 5x....0=x^2 +5x - 36

this is factorable to 0=(x+9)(x-4) set each equal to zero and x=(-9) and x=(4), but you cannot take the logarithm of a negative so the only solution is x=4