Question 841359
{{{ log( 10, x+1 ) - log( 10, x-6 ) = 1 }}}
{{{ log( 10, (x+1)/(x-6) ) = 1 }}}
Now make the substitution 
{{{ 1 = log( 10, 10 ) }}}
{{{ log( 10, (x+1)/(x-6) ) = log( 10,10 ) }}}
{{{ ( x+1 )/( x-6 ) = 10 }}}
{{{ x + 1 = 10x - 60 }}}
{{{ 9x = 61 }}}
{{{ x = 61/9 }}}
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check:
{{{ log( 10, x+1 ) - log( 10, x-6 ) = 1 }}}
{{{ log( 10, 61/9 + 1 ) - log( 10, 61/9 - 6 ) = 1 }}}
{{{ log( 10, 6.7778 + 1 ) - log( 10, 6.7778 - 6 ) = 1 }}}
{{{ log( 10, 7.7778 ) - log( 10, .7778 ) = 1 }}}
{{{ .89085 - ( -.10914 ) = 1 }}}
{{{  .99999 = 1 }}}
close enough