To solve equation

\(50=600e^{-0.4x}\)

\(\frac{50}{600}=e^{-0.4x}\)

taking ln of both sides we get

\(\ln(50/600)=\ln e^{-0.4x}\)

\(\ln0.08=\ln e^{-0.4x}\)

since \(\ln e^x=x\)

\(x=-\frac{(-2.53)}{0.4}\)

\(=6.32\)

Hence x=6.32

Result: x=6.32

\(50=600e^{-0.4x}\)

\(\frac{50}{600}=e^{-0.4x}\)

taking ln of both sides we get

\(\ln(50/600)=\ln e^{-0.4x}\)

\(\ln0.08=\ln e^{-0.4x}\)

since \(\ln e^x=x\)

\(x=-\frac{(-2.53)}{0.4}\)

\(=6.32\)

Hence x=6.32

Result: x=6.32