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.

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

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