SOLUTION: If the two roots of the quadratic equation x^2-6x+1=0 are log a and log b, what is the value of log(a,ab^2)+log(b,a^2b)? Thank You.

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Question 1105288: If the two roots of the quadratic equation x^2-6x+1=0 are log a and log b,
what is the value of log(a,ab^2)+log(b,a^2b)?
Thank You.

Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
can be solved by "completing the square"
or by using the quadratic formula.
Completing the square:






The expression becomes itself if we interchange a and b,
so it does not matter which root is and which root is .
Let us say that and .
Those are base 10 logarithms, so to get to base a and base b,
we use the "change of base formula."

.

Now we can calculate that expression

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