SOLUTION: log9 (4p2 - 7p + 53) = log3 (4p-3)

Question 389692: log9 (4p2 - 7p + 53) = log3 (4p-3)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
The approach here is to change the base 9 logarithm to a base 3 logarithm, using the change of base formula
log9 (4p2 - 7p + 53) = log3 (4p-3)
changing the left term to a base 3 logarithm,
log3 (4p2 - 7p + 53)/log3(9)
log3(9)=2
log3 (4p2 - 7p + 53)/2= log3 (4p-3)
(4p2 - 7p + 53)/2=(4p-3)
4p^2-7p+53=8p-6
4p^2-15P+59=0
solve using the following quadratic equation, with a=4, b=-15, and c=59
since the discriminate is negative, b^2-4*a*c =225-4*4*59=-719
there is no solution

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