Question 637911
(a) log(x+2) - log x = log(x + 16) - log (x + 2)
    log [(x + 2)/x] = log [(x + 16)/(x + 2)]
    {{{ (x + 2)/x = (x + 16)/(x + 2) }}}, cross multiply
        {{{ (x + 2)^2 = x(x + 16) }}}
        {{{ x^2 + 4x + 4 = x^2 + 16x}}}
        {{{ 12x = 4}}}
   Answer:     {{{highlight(x = 1/3)}}}  

(b) Let x be the first term and k be the common difference.
    6th term = x + 5k
    2nd term = x + k
    5th term = x + 4k

    Equations:
    (x + 5k) = 2(x + k) or x -  3k = 0
    (x + 4k) - x = 10 or 4k = 10, therefore k = 2.5
    So x - 3(2.5) = 0, therefore x = 7.5
    
Answer: The first term is  7.5 and the common difference is 2.5.