what is the f inverse of f(x)= ln(x-3)

Question

I got y= e^x - 4

Solve
8 times 10^(2x-7)=3

I do not know how to do this. Do i get 8 and 10 with the same base? How?

Thanks!

Answer 1

f(x) = ln(x-3) or
y = ln(x-3)

first step of find the inverse is to interchange the x and y variables, so the inverse is

x = ln(y-3)
e^x = y-3
y = e^x + 3

2.

8 (10^(2x-7) ) = 3
10^(2x-7) = .375
take log of both sides

log( 10^(2x-7) ) = log .375
(2x-7) log 10 = log .375, remember log 10 = 1
2x - 7 = log .375
x = (7 + log.375)/2 = appr 3.287