Question

Solve for x to nearest hundredth 10e^-3x=564

Answer 1

we have the exponential equation

`10e^(-3x)=564`

Solve for x

`e^(-3x)=(564)/(10)`

Apply ln on both sides

`\ln e^(-3x)=\ln (564)/(10)`

Applying property of log

`\begin{gathered} (-3x)\cdot\ln e=\ln (564)/(10) \\ \\ (-3x)=\ln (564)/(10) \end{gathered}`
`x=-(\ln (564)/(10))/(3)`

x=-1.34