Question

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

Answer 1

x = 0.16823611831

Explanation:

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

Therefore ln*e2x = ln*1.4

2x = 0.33647223662

x = 0.16823611831

Answer 2

Answer:
`x=0.168`

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:

`(2x)/(2)=(ln(1.4))/(2)\\\\x=0.1682`

Rounded to the nearest thousand:

`x=0.168`