If ln ⁡ a = 2 , ln ⁡ b = 3 , and ln ⁡ c = 5, evaluate the following:a) ln ⁡ ( a 4 b 3 c 4 ) = ?b) ln ⁡ a 4 b 1 c 1 = ?

Question

If   ln  ⁡  a  =  2  ,  ln  ⁡  b  =  3  ,   and   ln  ⁡  c  =  5, evaluate the following:a)   ln  ⁡  (            a      4                      b        3                    c        4              )  =  ?b)   ln  ⁡            a      4              b      1              c      1        =  ?

Kalmukujobvg · Accepted Answer

ln  ⁡  a  =  2  ,  ln  ⁡  b  =  3  ,  ln  ⁡  c  =  5a)   ln  ⁡  (            a      4                      b        3                    c        4              )  =  ln  ⁡  (      a    4    )  −  ln  ⁡  (      b    3        c    4    )    ∴  [  ln  ⁡  (  a      |    b  )  =  ln  ⁡  a  −  ln  ⁡  b  ]then   ln  ⁡  (            a      4                      b        3                    c        4              )  =  4  ln  ⁡  a  −  [  ln  ⁡      b    3    +  ln  ⁡      c    4    ]    =  4  ln  ⁡  a  −  ln  ⁡      b    3    −  ln  ⁡      c    4      =  4  ln  ⁡  a  −  3  ln  ⁡  b  −  4  ln  ⁡  cNow plug the values  ln  ⁡  (            a      4                      b        3                    c        4              )  =  4  (  2  )  −  3  (  3  )  −  4  (  5  )    =  8  −  9  −  20  =  −  21    ln  ⁡  (            a      4                      b        3                    c        4              )  =  −  21

ritualizi6zk · Accepted Answer

b)  ln  ⁡            a      4              b      1              c      1        =  ln  ⁡  (      a    4    b  c      )          1              /            2          =      1    2    ln  ⁡  (      a    4    b  c  )    =      1    2    [  ln  ⁡      a    4    +  ln  ⁡  b  +  ln  ⁡  c  ]    =      1    2    [  4  ln  ⁡  a  +  ln  ⁡  b  +  ln  ⁡  c  ]    =      1    2    [  4  ×  2  +  3  +  5  ]  =      1    2    [  8  +  8  ]    =  8    ln  ⁡            a      4        b    c    =  8

If In a = 2, In b = 3, and In c = 5, evaluate the following: a) ln ((a^4)/(b^3 c^4))=? b) ln sqrt(a^4 b^1 c^1)=?

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