Calculate: ln ⁡ ( x − 2 ) + ln ⁡ ( 2 x − 3 ) = 2 ln ⁡ x

Question

Calculate:  ln  ⁡  (  x  −  2  )  +  ln  ⁡  (  2  x  −  3  )  =  2  ln  ⁡  x

okuzala3ul · Accepted Answer

Use Power Rule:       log    b    ⁡      x          c        =  c      log    b    ⁡  x  ln  ⁡  (  x  −  2  )  +  ln  ⁡  (  2  x  −  3  )  =  ln  ⁡  (      x          2        )Use Product Rule:   ln  ⁡  (  x  y  )  =  ln  ⁡  x  +  ln  ⁡  y  .  ln  ⁡  (  (  x  −  2  )  (  2  x  −  3  )  )  =  ln  ⁡  (      x          2        )Cancel &quot;  ln&quot; on both sides.  (  x  −  2  )  (  2  x  −  3  )  =      x          2      Expand  2      x          2        −  7  x  +  6  =      x          2      Move all terms to one side.  2      x          2        −  7  x  +  6  −      x          2        =  0Simplify   2      x          2        −  7  x  +  6  −      x          2       to       x          2        −  7  x  +  6      x          2        −  7  x  +  6  =  0Factor       x          2        −  7  x  +  6   (  x  −  6  )  (  x  −  1  )  =  0Solve for   x  x  =  6  ,  1Check solutionWhen   x  =  1, the original equation   ln  ⁡  (  x  −  2  )  +  ln  ⁡  (  2  x  −  3  )  =  2  ln  ⁡  x does not hold true.We will drop   x  =  1 from the solution set.Therefore,  x  =  6

Calculate: ln(x-2)+ln(2x-3)=2lnx

Answered question

Answer & Explanation

New Questions in Trigonometry