47. Express g (x) = - log4 (2x) in the general form of a logarithmic function, f (x) = k + a logb (x-h). Identify a, b, h and k.

Answer: a = - 1

b = 4

h = 0

k = - 1/2

Step-by-step explanation:

g (x) = - log4 (2x) (considering that the 4 is a base of the logarithm)

f (x) = k + a logb (x-h) (considering that b is the base of the logarithm)

Note that in f, x do not have a coefficient, this way we have to remove it to find a, b, h and k, so:

g (x) = - log₄ (2x) = - (log₄2 + log₄x) = - (1/2 + log₄x) = - 1/2 - log₄x

a = - 1

b = 4

h = 0

k = - 1/2