Let a and b be real numbers greater than...

Let a and b be real numbers greater than 1 for which there exists a positive real number c, different from 1, such that `2(log_a c +log_b c)=9log_ab c`. Find the largest possible value of `log_a b`.

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Let a and b be real numbers greater than 1 for which there exists a positive real number c, different from 1, such that `2(log_a c +log_b c)=9log_ab c`. Find the largest possible value of `log_a b`.

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