Question

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

Answer 1

Answer:

x=0.996

Step-by-step 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

$e^{2x}=\frac{22}{3}$

Now we take 'ln' on both sides

$ln(e^{2x})=ln(\frac{22}{3})$

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

$(2x)ln(e)=ln(\frac{22}{3})$

The value of ln(e) = 1

$2x=ln(\frac{22}{3})$

Divide both sides by 2

$x=\frac{ln(\frac{22}{3})}{2}$

x= 0.996215082

Round to nearest thousandth

x=0.996