How do you find the inverse of f(x)=50,000(0.8)^x?

1 Answer
Dec 8, 2015

y=(log(x)-log(50000))/log(0.8)

Explanation:

write as : y=50000(0.8)^x

Taking logs:

log(y) = log(50000)+log(color(white)(.)(0.8)^xcolor(white)(.))

But log(color(white)(.)(0.8)^xcolor(white)(.)) is the same as xlog(0.8)

Thus
x=(log(y)-log(50000))/log(0.8)

Now swap the x'x and the y's giving:

y=(log(x)-log(50000))/log(0.8)