Prove if f ( x ) = ln ⁡ ( 1 − 1 x 2 ) then f ( 2 ) + f ( 3 ) + f ( 4 ) = ln ⁡ ( 5 / 8 )I have that: f ( x ) = ln ⁡ ( 1 − 1 x 2 ) I need to prove that f ( 2 ) + f ( 3 ) + f ( 4 ) = ln ⁡ ( 5 8 ) Indeed, I proved that f ( 2 ) + f ( 3 ) + f ( 4 ) = ln ⁡ ( 3 / 4 ) + ln ⁡ ( 8 / 9 ) + ln ⁡ ( 15 / 16 ) But couldn't derive ln ⁡ ( 5 / 8 ) using it.Any hint is welcome!

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Prove if   f  (  x  )  =  ln  ⁡      (    1    −          1              x        2              )   then   f  (  2  )  +  f  (  3  )  +  f  (  4  )  =  ln  ⁡  (  5      /    8  )I have that:  f  (  x  )  =  ln  ⁡      (    1    −          1              x        2              )  I need to prove that   f  (  2  )  +  f  (  3  )  +  f  (  4  )  =  ln  ⁡      (          5      8        )  Indeed, I proved that   f  (  2  )  +  f  (  3  )  +  f  (  4  )  =  ln  ⁡  (  3      /    4  )  +  ln  ⁡  (  8      /    9  )  +  ln  ⁡  (  15      /    16  ) But couldn&#039;t derive   ln  ⁡  (  5      /    8  ) using it.Any hint is welcome!

Crevani9a · Accepted Answer

f  (  x  )  =  ln  ⁡      (    1    −                  1                  x          2                      )    =  ln  ⁡      (                                        x            2                    −          1                          x          2                      )    ⇒  f  (  2  )  =  ln  ⁡      (                  3        4              )      f  (  3  )  =  ln  ⁡      (                  8        9              )      f  (  4  )  =  ln  ⁡      (                  15        16              )  Property 1:  log  ⁡      (    a    b    )    =  log  ⁡  (  a  )  +  log  ⁡  (  b  )                    f        (        2        )        +        f        (        3        )        +        f        (        4        )                            =        ln        ⁡                  (                                    3              4                                )                +        ln        ⁡                  (                                    8              9                                )                +        ln        ⁡                  (                                    15              16                                )                                                            =                      P            r            .            1                          ln        ⁡                  (                                    3              4                                ⋅                                    8              9                                ⋅                                    15              16                                )                                                  =        ln        ⁡                  (                                    5              8                                )                .

Prove if f ( x ) = ln ⁡ ( 1 −<!-- −

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