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Question

If log1218=a and log2454=b, then ab+5(ab) is equal to

A
1
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B
2
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C
3
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D
none of these
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Solution

The correct option is A 1
Given,
log1218=a,log2454=b

So alog218log212=log2(2×32)log2(22×3)=1+2log232+log23 (1)

b=log54log24=log2(2×33)log2(23×3)=1+3log233+log23 (2)

Solving eqs.(1) and (2) we get,
log23=2a12a=3b13b


Equating a and b in above equaion
(2a1)(3b)=(2a)(3b1)

6a2ab3+b=6b23ab+a6a6b+ba2ab+3ab3+2=0

5a5b+ab1=05(ab)+ab=1

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