Question

Solve the equation. Round to the
nearest thousandth.
4e2x = 5
x = [?]

Answer 1

0.112

Explanation:

The answer above me says 0.1116 but its actually 0.112

Answer 2

x = 0.1116 (rounded to 4 decimal places)

Explanation:

We need to isolate "e" first, so we do:

`4e^(2x)=5\\e^(2x)=(5)/(4)\\e^(2x)=1.25`

Solving these types of equations requires us to take the Natural Logarith (Ln) of both sides, so we have:

`e^(2x)=1.25\\Ln(e^(2x))=Ln(1.25)`

We can use the property of logarithms shown below to further simplify:

`Ln(a^b)=bLn(a)`

So, we have:

`Ln(e^(2x))=Ln(1.25)\\(2x)Ln(e)=Ln(1.25)`

We know Ln(e) = 1, thus now, we can replace it and solve for x:

`(2x)Ln(e)=Ln(1.25)\\(2x)(1)=Ln(1.25)\\2x=Ln(1.25)\\2x=0.2231\\x=(0.2231)/(2)\\x=0.1116`

So

x = 0.1116 (rounded to 4 decimal places)