given that (25^n+3 - 5^2n+4)/8 = 3^n 5^a where are a and n integers. find the value of n and of a

[tex]( {25}^{n + 3} - {5}^{2n + 4} ) \div 8 = {3}^{n} {5}^{a} \\ \frac{ {5}^{2n + 6} - {5}^{2n + 4} }{8} = {3}^{n} {5}^{a} \\ {5}^{6} \times {( {5}^{n} )}^{2} - {5}^{4} \times {( {5}^{n}) }^{2} = 8 \times {3}^{n} \times {5}^{a} \\ \frac{ {( {5}^{n} )}^{2}( {5}^{6} - {5}^{4})}{ {5}^{a} } = 8 \times {3}^{n} \\ \frac{ {( {5}^{n}) }^{2}. {5}^{4}( {5}^{2} - 1) }{ {5}^{a} \times 8} = {3}^{n} \\ {5}^{2n + 4 - a}= {3}^{n - 1} \\ log( {5}^{2n + 4 - a} ) = log( {3}^{n - 1} ) \\( 2n + 4 - a) log(5) =( n - 1) log(3) \\ \frac{2n + 4 - a}{n - 1} = log_{5}(3) \\ log(5) = n - 1 \\ n = log(5) + log(10) = log(50) \\ 2( log(50) ) + 4 - a = log(3) \\ a = 2 \times log(50) - log(3) + 4 \\ a = log( \frac{ {50}^{2} }{3} ) + log( {10}^{4} ) \\ a = log( \frac{ {50}^{2} }{3} \times {10}^{4} ) [/tex]
apakah seperti maksudnya....