inverse with log problem?

Question

i need to find the inverse of:
f(x)=2-3 log (base 4) (y+1)

i need the work to go with it too... thanks

Answer 1

I'm sure you mean f(x)=2-3 log (base 4) (x+1) as this is a function of x.

Write as y=2-3 log (base 4) (x+1), then exchange x and y to get the inverse.

x=2-3 log (base 4) (y+1)

This is the inverse function, but we would like to write it in function notation, so we solve for y:
(x-2)/(-3)=log (base 4) (y+1)
4^((x-2)/(-3)) = y+1
4^((x-2)/(-3)) - 1 = y

Answer 2

Assuming you meant

f(x) = 2 - 3log(4)(x + 1)
y = 2 - 3log(4)(x + 1)

because if it isn't, then your function is wrong.

x = 2 - 3log(4)(y + 1)
x - 2 = -3log(4)(y + 1)
-(x - 2)/3 = log(4)(y + 1)
4^(-(x - 2)/3) = y + 1
y = -1 + 4^(-(x - 2)/3)

ANS : f(x)^-1 = 4^(-(x - 2)/3) - 1