Combine the constants:

Isolate the exponential function by dividing:

Take the natural log of both sides:

Finally isolate x:

First, let's begin by simplifying the left hand side.

becomes and becomes . Remember that , and the in that expression can come out to the front, as in .

Now, our expression is

From this, we can cancel out the 2's and an x from both sides.

Thus our answer becomes:

.

Combine the constants:

Isolate the exponential function by dividing:

Take the natural log of both sides:

Finally isolate x:

Combine the constants:

Isolate the exponential function by dividing:

Take the natural log of both sides:

Finally isolate x:

First, let's begin by simplifying the left hand side.

becomes and becomes . Remember that , and the in that expression can come out to the front, as in .

Now, our expression is

From this, we can cancel out the 2's and an x from both sides.

Thus our answer becomes:

.

First, let's begin by simplifying the left hand side.

becomes and becomes . Remember that , and the in that expression can come out to the front, as in .

Now, our expression is

From this, we can cancel out the 2's and an x from both sides.

Thus our answer becomes:

.

The key to this is that . From here, the equation can be factored as if it were .

and

and

and

Now take the natural log (ln) of the two equations.

and

and

The key to this is that . From here, the equation can be factored as if it were .

and

and

and

Now take the natural log (ln) of the two equations.

and

and

In order to condense the logarithmic expression, we use the following properties

As such

We expand logarithms using the same rules that we use to condense them.

Here we will use the quotient property

and the power property

.

Use the quotient property:

Rewrite the radical:

Now use the power property: