SOLUTION: How do I solve the logarithmic equation symbolically, log x^8=7+2 log x, we did not go over this in class? v/r Dean

Question 21612: How do I solve the logarithmic equation symbolically, log x^8=7+2 log x, we did not go over this in class?
v/r Dean
Answer by NaiXLG(18) (Show Source): You can put this solution on YOUR website!
Ahhhh yes, logarithims, gotta love 'em...

So, you begin by writing the original question
Solve for x:

So, begin by rewriting the right logarithim as because the properties of logarithims states that

So now you should have,

Bring the right logarithim to the left, so now we have all logs on the left, and all non-logs (constants) on the right.

Now using yet another property of logarithims, go ahead and simplify that left side into one single log....
Remember
So, you'll have;

Now, use your properties of exponents to simplify that log a little more...
Remember
So,

Now, because the log has a base of ten, raise both sides of the equation to the tenth power....

The log cancels out, and you're left with

Now simply take the 6th root of x to make it just a single x, and no more, and take the 6th root of as well. (What you do to one side of the equation, you must do to the other.)

There you go....!

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