Question 1024741
{{{ log( 2, 3x-1 ) - 1  = log( 2, x ) }}}
Use the identity:
{{{ 1 = log( 2,2 ) }}}
Now you have:
{{{ log( 2, 3x-1 ) - log( 2,2 )  = log( 2, x ) }}} 
{{{ log( 2, ( 3x - 1 )/2 ) = log( 2,x ) }}}
if the logs are equal, the quantities are equal
{{{ ( 3x - 1 )/2 = x }}}
{{{ 3x - 1 = 2x }}}
{{{ x = 1 }}}
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check answer:
{{{ log( 2, 3x-1 ) - 1  = log( 2, x ) }}}
{{{ log( 2, 3*1-1 ) - 1  = log( 2,1 ) }}}
{{{ log( 2, 2 ) - 1 = log( 2,1 ) }}}
{{{ 1 - 1 = 0 }}}
{{{ 0 = 0 }}}