Answer
$y=Ce^{-4x}+3$
Work Step by Step
Subtract by $\ln{C}$ on both sides:
$\ln{(y-3)} - \ln{C}=-4x$
RECALL:
For positive real numbers M and N:
$\ln{M} - \ln{N} = \ln{\left(\dfrac{M}{N}\right)}$
Use the rule above to obtain:
$\ln{\left(\dfrac{y-3}{C}\right)}=-4x$
RECALL:
$\ln{M}= y \longrightarrow e^y=M$
Use the rule above to obtain:
$e^{-4x}=\dfrac{y-3}{C}$
Multiply by $C$ on both sides of the equation to obtain:
$C \cdot e^{-4x} = C \cdot \dfrac{y-3}{C}
\\Ce^{-4x} = y-3
\\y-3=Ce^{-4x}$
Add $3$ to both sides of the equation to obtain:
$y-3+3 = Ce^{-4x}+3
\\y=Ce^{-4x}+3$
