Find the solution of the equation 5^(11x-1)=7^x

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We have to find the solution of 5^(11x-1)=7^x

5^(11x-1)=7^x

=> 5^11x / 5 = 7^x

take the logarithms of both the sides

log( 5^11x / 5) = log 7^x

=> log 5^11x - log 5 = x log 7

=> 11x log 5 - log 5 = x log 7

=> 11x log 5 - x log 7 = log 5

=> x( 11*log 5 - log 7) = log 5

=> x = log 5 / ( 11*log 5 - log 7)

=> x = 0.102 approximately.

Therefore x = log 5 / ( 11*log 5 - log 7)

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