Simplify the fractionsFirst, I apologize for the title, but if I write my question then the characters will be too long.Here's my question:Why ( log ⁡ 3 log ⁡ 2 + 2 log ⁡ 3 2 log ⁡ 2 ) ( 2 log ⁡ 2 log ⁡ 3 + log ⁡ 2 2 log ⁡ 3 ) = ( 2 × log ⁡ 3 log ⁡ 2 ) ( 5 2 × log ⁡ 2 log ⁡ 3 )?I have no idea how the left side becomes the right side.

Question

Simplify the fractionsFirst, I apologize for the title, but if I write my question then the characters will be too long.Here&#039;s my question:Why   (            log      ⁡      3              log      ⁡      2        +            2      log      ⁡      3              2      log      ⁡      2        )  (            2      log      ⁡      2              log      ⁡      3        +            log      ⁡      2              2      log      ⁡      3        )  =  (  2  ×            log      ⁡      3              log      ⁡      2        )  (      5    2    ×            log      ⁡      2              log      ⁡      3        )?I have no idea how the left side becomes the right side.

Azul Lang · Accepted Answer

Because            log      ⁡      3              log      ⁡      2        +                    2            log      ⁡      3                      2            log      ⁡      2        =            log      ⁡      3              log      ⁡      2        +            log      ⁡      3              log      ⁡      2        =  2            log      ⁡      3              log      ⁡      2      and similarly            2      log      ⁡      2              log      ⁡      3        +            log      ⁡      2              2      log      ⁡      3        =  2            log      ⁡      2              log      ⁡      3        +      1    2              log      ⁡      2              log      ⁡      3        =      (    2    +          1      2        )              log      ⁡      2              log      ⁡      3        =      5    2              log      ⁡      2              log      ⁡      3

drobtinicnu · Accepted Answer

multiplying this out and simplify:            log      ⁡      3      ⋅      2      log      ⁡      2              log      ⁡      2      ⋅      log      ⁡      3        +            4      log      ⁡      3      ⋅      log      ⁡      2              2      log      ⁡      2      ⋅      log      ⁡      3        +            log      ⁡      3      ⋅      log      ⁡      2              log      ⁡      2      ⋅      2      log      ⁡      3        +            2      log      ⁡      3      ⋅      log      ⁡      2                      2        2            log      ⁡      2      ⋅      log      ⁡      3        =  .  .  .

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