Question

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

Answer 1

Answer:

x = 0.1116 (rounded to 4 decimal places)

Step-by-step explanation:

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

$4e^{2x}=5\\e^{2x}=\frac{5}{4}\\e^{2x}=1.25$

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:

$(2x)Ln(e)=Ln(1.25)\\(2x)(1)=Ln(1.25)\\2x=Ln(1.25)\\2x=0.2231\\x=\frac{0.2231}{2}\\x=0.1116$

So

x = 0.1116 (rounded to 4 decimal places)

Answer 2

Answer:

0.112

Step-by-step explanation:

The answer above me says 0.1116 but its actually 0.112