Solve this:

Q. If  log 7 12   = a   ,   log 12   24   = b  . Find  log 54 168 , in terms of a and b. 

Dear Student

Givenlog712=aand log1224=blog224log212=log23.3log222.3                  =3log22+log232log22+log23               logmn=logm+logn        b         =3+log232+log23                logaa=1 b2+log23=3+log232b+blog23=3+log23blog23-log23=3-2blog23b-1=3-2blog23=3-2bb-1-----(i)Now168=24×7Applying log we getlog12168=log1224+log127               =b+1a                =ab+1aand log1254=log54log12=log233×2log222×3                                          =3log23+log222log22+log23                        logmn=logm+logn                         =3log23+12+log23                                 logaa=1Now substituting (i)  i.e.,log23=3-2bb-1 we get            =33-2bb-1+12+3-2bb-1          =9-6b+b-12b-2+3-2b          =8-5b1=8-5blog54168=log12168log125                    =ab+1a8-5b            
Regards

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