Answer: [tex]x=0.168[/tex]
Step-by-step explanation:
To solve the equation [tex]e^{2x}=1.4[/tex] you need to apply natural logarithm to both sides of the equation:
[tex]ln(e)^{2x}=ln(1.4)[/tex]
According to the logarithms property:
[tex]ln(b)^a=aln(b)[/tex]
Then, applying the property, you get:
[tex](2x)ln(e)=ln(1.4)[/tex]
You need to remember the following:
[tex]ln(e)=1[/tex]
Therefore:
[tex]2x(1)=ln(1.4)\\\\2x=ln(1.4)[/tex]
And finally, you must divide both sides of the equation by 2:
[tex]\frac{2x}{2}=\frac{ln(1.4)}{2}\\\\x=0.1682[/tex]
Rounded to the nearest thousand:
[tex]x=0.168[/tex]
