Question

Hi could somebody please help me answer this question? Thank youuu

Answer 1

Given:

$\ln(y-8)=-2x+\ln C$

To find:

y as a function of x.

Solution:

We have,

$\ln(y-8)=-2x+\ln C$

It can be written as

$\ln(y-8)=\ln e^{-2x}+\ln C$           $[\because \ln e^x=x]$

$\ln(y-8)=\ln (Ce^{-2x})$           $[\because \ln (ab)=\ln a+\ln b]$

On comparing both sides, we get

$y-8=Ce^{-2x}$

Adding 8 on both sides, we get

$y=Ce^{-2x}+8$

Therefore, the equation function is $y=Ce^{-2x}+8$.