Question 1065101
I'll say {{{ y = g(x) }}}
{{{ y = log( 7, ( (2/3)x - 1 ) ) }}}
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Raising the base {{{ 7 }}} to any log, either + or -
cannot result in a negative number for the result,
{{{ (2/3)x - 1 }}}, so I conclude that 
{{{ (2/3)x - 1 >= 0 }}}
{{{ (2/3)x >= 1 }}}
{{{ x >= 3/2 }}}
This is the domain
Here's the plot:
{{{ graph( 500, 500, -5, 5, -3, 3, log( 7, (2/3)*x  - 1 ) ) }}}