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Logarithm
1.Which of the following statements is not correct?

Answer:Option 1

Explanation:

Solution:
A = Since logaa=1, so log1010=1B=log(2+3)=5and log(2×3)=log6=log2+log3log(2+3)log(2×3).C= Since loga1=0,so log101=0.D = log(1+2+3)= log6= log(1×2×3)= log1+ log2+ log3.So (2) is incorrect

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2.If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:

Answer:Option 1

Explanation:

Solution:
log5512=log512log5=log29log(102)=9log2log10log2=(9×0.3010)10.3010=2.7090.699=2709699=3.876

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3.
log8log8
is equal to:

Answer:Option 1

Explanation:

Solution:
log8log8=log(8)log812=12log8log8=12

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4.
Iflogab+logba=log(a+b),then:

Answer:Option 1

Explanation:

Solution:
logab+logba=log(a+b)log(a+b)=log(ab×ba)=log1So,a+b=1

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5.
Iflog107=a,thenlog10(170)isequalto

Answer:Option 1

Explanation:

Solution:
log10(170)=log101log1070=log10(7×10)=(log107+log1010)=(a+1)

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6.If log10 2 = 0.3010, then log2 10 is equal to:

Answer:Option 1

Explanation:

Solution:
log210=1log102=10.3010=100003010=1000301

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7.If log10 2 = 0.3010, the value of log10 80 is:

Answer:Option 1

Explanation:

Solution:
log1080=log10(8×10)=log108+log1010=log10(23)+1=3log102+1=(3×0.3010)+11.9030

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8.
Thevalueof(1log360+1log460+1log560)is:

Answer:Option 1

Explanation:

Solution:
Given expression
=log603+log604+log605=log60(3×4×5)=log6060=1

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9.If log 2 = 0.30103, the number of digits in 264 is:

Answer:Option 1

Explanation:

Solution:
log(264)=64×log2=(64×0.30103)=19.26592
Its characteristic is 19.
Hence, then number of digits in 264 is 20.

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10.
Iflogx(916)=12,thenxisequalto:

Answer:Option 1

Explanation:

Solution:
logx(916)=12x12=9161x=916x=169x=(169)2x=25681

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