given that loga  (3x-4a)+loga  3x=2/(log2  a)+loga (1-2a),where 0<a<1/2 ,find x  

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You need to use logarithmic identities, hence, you may convert the sum of logarithms from the left into a logarithm of product such that:

`log_a (3x(3x - 4a)) = 2/(log_2 a) + log_a (1 - 2a)`

You need to remember that `log_a b = 1/(log_b a)`  such that:

`log_a (3x(3x - 4a)) = 2/(1/(log_a 2)) + log_a (1 - 2a)`

`log_a (3x(3x - 4a)) = 2log_a 2 + log_a (1 - 2a)`

`log_a (3x(3x - 4a)) = log_a (2^2) + log_a (1 - 2a)`

You may convert the sum of...

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