Solve for x: log base 64 25x-log base 64 (x-7)=2/3

The equation is 

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First, from the rule , we rewrite the left hand side as:

           .

Now we write the right hand side as a log with base 64, so that we can make the arguments equal, setting a new equation.

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We can simplify the argument of this expression into a more manageable expression using the laws of exponents:

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Thus, from  we clearly have:

                                 .

 For x different from 7:

                                       25x=16(x-7)
            
                                       25x=16x-112

                                         9x=-112
                                 
                                           x=-112/9.

This value is approximately -12.44, so x-7, the argument of both the first and the second expression, would be negative. Thus, the equation has no solution.