SOLUTION: How would I solve the below problem...THX tutors!!! :) log(16)X + log(8)X + log(4)X + log(2)X = 6 (the 16, 8, 4, and 2 are all smaller numbers)

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Use the rule for base conversion:

So: , but since we know that if then , so means that . Solving for gives us , so . That means that .

Using a similar process, we get:

and

Now we can write:


Applying the common denominator of 12:


Simplifying:



Therefore

That is the exact answer. You can use the x^y function on your Windows calculator in scientific mode to calculate a numerical approximation.

You can put this solution on YOUR website!
How would I solve the below problem...THX tutors!!! :)

Use the 'change of base' formula:



on each of the first three terms on the left, using  as the 


 
Now we can evaluate those three denominators by using the definition of
logarithm:

    is equivalent to 

For , we set it equal to the unknown "y":



Then it is equivalent to  or , so ,
therefore   

------

For , we set it equal to the unknown "z":



Then it is equivalent to  or , so ,
therefore  

------

For , we set it equal to the unknown "w":



Then it is equivalent to  or , so ,
therefore  

------

Substitute these for the first three terms of:





Clear of fractions by multiplying every term by LCD = 12









Divide both sides by 25





Now use the definition of logarithm again to rewrite
that as



Find that on a TI calculator by typing 

2^(72/25)

then pressing ENTER

  

Edwin