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​ log3 54 / log486 3   -   log31458 /log183

Dear Student,
Please find below the solution to the asked query:

log354log4863-log31458log183=log354×log3486-log31458×log318          As, logab=1logba=log333×2×log335×2-log336×2×log332×2=log333+log32×log335+log32-log336+log32×log332+log32         As, logxab=logxa+logxb=3log33+log32×5log33+log32-6log33+log32×2log33+log32          As, logxab=b logxa=3+log32×5+log32-6+log32×2+log32             As, log33=1=15+3log32+5log32+log322-12+6log32+2log32+log322=15+3log32+5log32+log322-12-6log32-2log32-log322=3+8log32-8log32=3

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