Question

Use natural logarithms to solve the equation. e2x = 1.4 Round to the nearest thousandth.

Answer 1

Answer: $x=0.168$

Step-by-step explanation:

To solve the equation $e^{2x}=1.4$ you need to apply natural logarithm to both sides of the equation:

$ln(e)^{2x}=ln(1.4)$

According to the logarithms property:

$ln(b)^a=aln(b)$

Then, applying the property, you get:

$(2x)ln(e)=ln(1.4)$

You need to remember the following:

$ln(e)=1$

Therefore:

$2x(1)=ln(1.4)\\\\2x=ln(1.4)$

And finally, you must divide both sides of the equation by 2:

$\frac{2x}{2}=\frac{ln(1.4)}{2}\\\\x=0.1682$

Rounded to the nearest thousand:

$x=0.168$

Answer 2

Answer:

x = 0.16823611831

Step-by-step explanation:

ln (natural log), when multiplied by e, cancels it out.

Therefore ln*e2x = ln*1.4

2x = 0.33647223662

x = 0.16823611831