If f(x) = (4/3)ln(7x/5), then f^-1(x) =?

Question

If f(x) = (4/3)ln(7x/5), then f^-1(x) =?


possible solutions....

a. (7/5)e^(4x/3)

b. (7/4)e^(5x/3)

c. (7/4)e^(3x/5)

d. (5/3)e^(7x/4)

e. (5/7)e^(3x/4)

f. (4/5)e^(7x/3)

g. (3/4)e^(5x/7)

h. (3/4)e^(7x/5)

i. (3/7)e^(4x/5)

Answer 1

f(x) = (4/3)ln((7x)/5)

x = (4/3)(ln((7(f(x)^-1)/5)
3x = 4ln((7(f(x)^-1)/5)
(3/4)x = ln(7(f(x)^-1)/5)
e^((3/4)x) = 7(f(x)^-1)/5
5e^((3/4)x) = 7f(x)^-1
f(x)^-1 = (5/7)e^((3/4)x)

ANS : e.) (5/7)e^(3x/4)

Answer 2

I'm leaning towards h. If that's wrong, it's g.