Solve this: Q. If log 7 12 = a , log 12 24 = b . Find log 54 168 , in terms of a and b. Share with your friends Share 0 Koka Sri Lakshmi Divya Sai answered this Dear Student Givenlog712=aand log1224=b⇒log224log212=log23.3log222.3 =3log22+log232log22+log23 ∵logmn=logm+logn b =3+log232+log23 ∵logaa=1 ⇒b2+log23=3+log23⇒2b+blog23=3+log23⇒blog23-log23=3-2b⇒log23b-1=3-2b⇒log23=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=8-5b⇒log54168=log12168log125 =ab+1a8-5b Regards -1 View Full Answer