Question

Convert the given function into a logarithmic function f(x)=8.71e^-0.55x

Answer 1

I have this so far
f(x)=8.71e^-0.55x
y=8.71e
6-0.55x
y/8.71 =e^-0.55x

In y-In 8.71 = In e^-0.55x

Answer 2

use rules of logs to combine the two terms on the right? and cancel the ln e?

Answer 3

Can you show me how to do this?

Answer 4

ln a - ln b = ln (a/b)

Answer 5

ln e^a=a

Answer 6

\[f(x)=8.71e^{-0.55x}\]
let f(x)=y
\[y=8.71e^{-0.55x} \\ \\ \ln(y)=\ln(8.71e^{-0.55x})\]
Using ln(ab)=ln(a)+ln(b)
\[\ln(y)=\ln(8.71)+\ln(e^{-0.55x})\]
Also, \(ln(e^m)=m\), so
\[\ln(y)=\ln(8.71)-0.55x\]