Simplifying using the rule of logsHow would you simplify: [ 16 5 ln ⁡ ( x + 2 ) − 1 5 ln ⁡ ( x − 3 ) − ln ⁡ x ] 4 6 and put it in the form ln ⁡ m n . Stating the values of m and n.

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Simplifying using the rule of logsHow would you simplify:             [              16        5            ln      ⁡      (      x      +      2      )      −              1        5            ln      ⁡      (      x      −      3      )      −      ln      ⁡      x      ]        4    6   and put it in the form   ln  ⁡      m    n  . Stating the values of m and n.

DelmagnoIHb · Accepted Answer

The expression evaluated at   x  =  6 is      16    5    ln  ⁡  8  −      1    5    ln  ⁡  3  −  ln  ⁡  6  =      48    5    ln  ⁡  2  −      1    5    ln  ⁡  3  −  ln  ⁡  2  −  ln  ⁡  3  =      43    5    ln  ⁡  2  −      6    5    ln  ⁡  3Evaluated at   x  =  4 it is      16    5    ln  ⁡  6  −      1    5    ln  ⁡  1  −  ln  ⁡  4  =      16    5    ln  ⁡  2  +      16    5    ln  ⁡  3  −  2  ln  ⁡  2  =      6    5    ln  ⁡  2  +      16    5    ln  ⁡  3Thus the difference is      43    5    ln  ⁡  2  −      6    5    ln  ⁡  3  −      6    5    ln  ⁡  2  −      16    5    ln  ⁡  3  =      37    5    ln  ⁡  2  −      22    5    ln  ⁡  3  =      1    5    ln  ⁡            2              37                    3              22            There&#039;s no way to represent it as   ln  ⁡  (  m      /    n  ), because this would mean            (              m        n            )                    5        =            2              37                    3              22            and this is impossible with integer m and n.

Simplifying using the rule of logs How would you simplify: [(16)/5 ln(x + 2) - 1/5 ln(x - 3) - ln x]_4^6 and put it in the form ln(m/n). Stating the values of m and n.

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