Solve for :
Well, we are given:
Well, let's deal with the right side first, they are currently in different bases, therefore we must change the bases by using the change of base formula:
Where we are using base 10 because the right side has a base 10 logarithm.
Therefore we get:
Where:
and
(They are very close together, where the first difference is in the ten thousandths place.)
So we get:
There's really not an easy way to solve this, so I'm going to make the following approximation:
You get:
To verify:
And there you go.
With equations have orders that high, there are very few differences. As a matter of fact, with the equation that I had before(the wrong one), it had all of its roots at (4,0).
Just for fun:
Now if we take and multiply we get:
And that also yields 4 as it's only zero.