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Question

If log35=a and log32=b then log3300=


A

2(a+b)

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B

2(a+b+1)

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C

2(a+b+2)

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D

(a+b+4)

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E

(a+b+1)

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Solution

The correct option is B

2(a+b+1)


Explanation for the correct option:

Given that log35=a and log32=b

We know that logb(xy)=logb(x)+logb(y)

So, log3300 can be simplified as log33×102

=log332+log3(5×2)2=2log33+2log3(5×2)[logb(x)n=nlogb(x)]=2log33+2log3(5)+2log3(2)[logb(xy)=logb(x)+logb(y)]=2(1)+2(a)+2(b)[logb(b)=1,log3(5)=a,log3(2)=b]=2(a+b+1)

Hence, option(B) i.e. 2(a+b+1), is the correct answer.


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