Question

E^{2-3 x}=125 solve for x

Answer 1

The given equation

`e^((2-3x))=125`

Insert ln on both sides

`ln(e^(2-3x))=ln125`

Use the power rule

`(2-3x)ln(e)=ln(125)`

Substitute ln(e) by 1

`2-3x=ln(125)`

Subtract 2 from each side

`\begin{gathered} 2-2-3x=-2+ln(125) \\ \\ -3x=-2+ln(125) \end{gathered}`

Multiply all terms by -1

`3x=2-ln(125)`

Divide both sides by 3

`\begin{gathered} (3x)/(3)=(2-ln(125))/(3) \\ \\ x=(2-ln(125))/(3) \\ \\ x\approx-0.943 \end{gathered}`