Question 6629
First up, use the property {{{ log(b,a) - log(b,c) = log(b,(a/c)) }}}.


So using that, {{{ log(9,((b+4)/(b-3))) = log(9,8) }}}


Since both sides of the equation are log base 9, we can simply say 


{{{ (b+4)/(b-3) = 8 }}}


{{{ b + 4 = 8(b - 3) }}} <---- multiply both sides by (b-3)


{{{ b + 4 = 8b - 24 }}} <---- Solve for b


{{{ 28 = 7b }}} <----- combine like terms across equals sign


{{{ b = 4 }}} <---- finally solve for b