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Question

If a=log1218, b=log2454 then the value of ab+5(a-b) is


A

0

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B

4

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C

1

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D

None of these

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Solution

The correct option is C

1


We have

a=log1218=log218log212=1+2log232+log23 and

b=log2454=log254log224=1+3log233+log23.

Putting x=log23, we haveab+5(ab)=1+2x2+x.1+3x3+x+(1+2x2+x1+3x3+x)=6x2+5x+1+5(x2+1)(x+2)(x+3)=x2+5x+6(x+2)(x+3)


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