Question 615923
{{{ 7^(x/2) = 5^(1-x)  }}}
{{{ 7^(x/2) = 5^1*5^(-x) }}}
{{{ 7^(x/2) = 5/5^x }}}
Square both sides
{{{ 7^x =  25 / 5^(2x) }}}
{{{ 7^x * 5^(2x) = 25 }}}
{{{ 7^x * 5^x * 5^x  = 25 }}}
{{{ ( 7*5*5 )^x = 25 }}}
{{{ 175^x = 25 }}}
{{{ x * log( 175 ) = log( 25 ) }}}
{{{ x = log(25) / log(175) }}}
{{{ x = 1.39794 / 2.24304 }}}
{{{ x = .62323 }}}
check:
{{{ 7^(x/2) = 5^(1-x)  }}}
{{{ 7^(.62323/2) = 5^(1-.62323)  }}} 
{{{ 7^.31162 = 5^.37677 }}}
{{{ 1.83379 = 1.83379 }}}
OK