Question

Use natural logarithms to solve the equation. Round to the nearest thousandth. 3e^2x +5=27

Answer 1

x=0.996

Explanation:

`3e^(2x) +5=27`

To take natural log ln , we need to get e^2x alone

Subtract 5 on both sides

`3e^(2x)=22`

Now we divide both sides by 3

`e^(2x)=(22)/(3)`

Now we take 'ln' on both sides

`ln(e^(2x))=ln((22)/(3))`

As per log property we can move exponent 2x before ln

`(2x)ln(e)=ln((22)/(3))`

The value of ln(e) = 1

`2x=ln((22)/(3))`

Divide both sides by 2

`x=(ln((22)/(3)))/(2)`

x= 0.996215082

Round to nearest thousandth

x=0.996