Find gx the inverse of fx log402 Solutiony log2 4x 2 y 2

Find g(x), the inverse of f(x) = log(40-2.

Solution

y = log₂ (4x) - 2

y -2 = log (4x) / log 2

(y-2) log 2 = log (4x)

0.3 (y - 2) = log 4x

0.3 y - 0.6 = log 4x

antilog ( 0.3 y - 0.6 ) = 4x

x = [antilog (0.3 y - 0.6 )]/4

g(x) = [antilog (0.3 x - 0.6 )]/4