(a)      With the aid of four-figure logarithm tables, evaluate
          (0.004592).1/3.

(b)     If log10y + 3log10x  =  2, express y in terms  of x.

(c)      Solve the equations:
                   3x – 2y  =  21
                   4x  +  5y  =  5.

observation

The (a) and (c) parts were very well handled by most candidates but the (b) part was not handled well.  They were expected to state thus:

(a)      Log (0.004592) from the tables gives 3.6620.  Hence from the law of logarithms, log(0.004592)1/3  =  3.6620 ÷ 3  =  1.2207.  The antilog from the tables give 0.1663.

(b)     Log10y  +  3log10x  =  2  implies that log10yx³  =  log10100.
          Hence yx³  =  100.  Thus  y  =  100/x³.

(c)      Multiplying 3x – 2y  =  21  by  5 and multiplying  4x  +  5y  =
5 by 2, enables us to eliminate  y.  Thus by solving
x  =  5.  By substituting for  x  in any of the equation  y  =  -3.