Solve for x ? 2e^2x=4

2 Answers
Feb 20, 2018

x=ln(2)/2x=ln(2)2

Explanation:

2 e^(2x)=42e2x=4

e^(2x)=2e2x=2

Put the natural log function around both sides:

ln( e^(2x))=ln(2)ln(e2x)=ln(2)

Recall the exponential logarithm property which states that

log( a^x)=xlog(a)log(ax)=xlog(a)

and apply it here:

2xln(e)=ln(2)2xln(e)=ln(2)

ln(e)=1ln(e)=1 , this is from the basic definition of the natural log function.

ln(e)= log_e e=1ln(e)=logee=1

since e^1=ee1=e.

So

2x=ln(2)2x=ln(2)

x=ln(2)/2x=ln(2)2

Feb 20, 2018

x=ln2/2~~0.35x=ln220.35

Explanation:

I'm assuming that your problem is

2e^(2x)=42e2x=4

In this case, we first have to divide by 22 to get

e^(2x)=2e2x=2

If we now take the natural log of both sides, we get

ln(e^(2x))=ln2ln(e2x)=ln2

Let y=2xy=2x

<=>ln(e^y)=ln2ln(ey)=ln2

Recall that, ln(e^y)=yln(ey)=y

:.y=ln2

Substituting back y=2x, we get

2x=ln2

Now, we just have to divide by 2 to isolate x:

x=ln2/2

Using a calculator, this yields 0.34657...~~0.35