x = 4.
log(x) + log(x+5) = log(6x +12)
log x(x +5) = log(6x + 12)
Therefore x(x + 5)= 6x +12
x^2 + 5x - 6x - 12 = 0
x^2 - x - 12 = 0
(x - 4)(x + 3) = 0
x = -3, 4.
logs of negative values do not exists so the anser is x = 4.
d) by the cross product property, ab^2 = bc multiplied by ad
we are given
in the given triangle abc
angle a is 90° and segment ad is perpendicular to segment bc
we can see that
triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)
so, triangles(abc) and abd are similar
since, they are similar
so, the ratio of their sides must be equal
now, we can cross multiply
and we get
so, this could be step to prove it