# Solve for x using log50=600e^{-0.4x}

Question
Logarithms
Solve for x using $$\log50=600e^{-0.4x}$$

2021-01-26
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

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