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a =Log 12 18, b=log 24 54 find the value of ab+5(a-b)

a =Log12 18, b=log2454 find the value of ab+5(a-b)

Grade:12

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
Please find the answer to your question below
a=log12 18 b=log24 54
let x=18 and y=12
so log x=log(2*32)=log 2+2log3
similarly log y=2log2+log3
so a=logx/logy ; b=(log3+logx/log2+logy)
now ab+5(a-b)=
=(logx(log3+logx)/logy(log2+logy))+5((logx/logy)-(log3+logx/log2+logy))
by taking lcm and simplifying we get
=(5log2log3+(log3)2+6(log2)2)/((2log2log3)(3log2+log3))
=(5log2log3+(log3)2+6(log2)2)/(5log2log3+(log3)2+6(log2)2)
=1

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