Given f(x)=3(4^x), what is f^−1 (x)?

Answer 1

y = 3 * 4^x
becomes
x = 3 * 4^y
4^y = x/3
y log 4 = log (x/3) = log x - log 3
y = (log x - log 3) / log 4

Answer 2

f(x)=3(4^x)
or
y = 3(4^x)
step1: to form the inverse equation, interchange the x and y
x = 3(4^y)
x/3 = 4^y
take log of both sides
log(x/3) = log(4^y)
logx - log3 = ylog4
y = (logx - log3)/log4 ---> f^-1 (x) = (logx - log3)/log4