# 2^x = 3

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### 5 Answers

We can use the property for the natural logarithm:

`lna^b = m ` `<=>` `blna = m`

Applying the property above in our problem, we will have:

`ln2^x = ln3`

`xln2 = ln3`

Isolate the x on left side using the opposite operation of Multiplication, which is Division.

Divide both sides by ln2.

`x = ln3/ln2`

That is it! :)

2^x=3

This can be solved a couple different ways, but the way that I learned was to use a natural log or ln.

ln(2^x)=ln3

You can now use the log rule where you make the exponent a coefficient.

xln2=ln3

To get x by itself you divide and end up with x=ln3/ln2

`2^x = 3`

`ln2^x = ln3`

`xln2 = ln3`

`x = ln3 / ln2`

``Exploit the natural log (ln)to make this problem easier. First take the natural log of both sides. Then you'll see that the exponent can be brought down since that is a property of logs. Then its simply a matter of isolating x.

You have to use the property of logs to solve this:

`2^x = 3`

`ln (2^x) = ln3`

`x ln2 = ln3`

`x = ln3 / ln2`

``

2^x=3

x=square root(2)

x=1.4142

2^square root(2)= 3