To prove: 

Here goes:

Let 

Change that log equation to its 
equivalent exponent form:



Now take logs base 10 of both sides:





Use the "jump-over" rule of logarithms where the exponent
"jumps over both its base and the word "log" and turns into a
multiplier. Like this:



See how the x jumped over the "8" and the "log" and became
a multiplier instead of being an exponent. 

Now we divide both sides by  to solve for x.



And now we go back and remember what x was -- we let 

So we have:



and it's proved.

Edwin