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Log of a number from its prime factors, using given log values (log 2, log 3 or p, q, r)

This type of question, asked 4 times: CDS 2 2017, CDS 2 2018, CDS 1 2021, CDS 1 2026. All 4 questions below, oldest first.

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  1. Question 1

    CDS 2 2017

    36
    If log⁡106=0.7782\log_{10} 6 = 0.7782 and log⁡108=0.9031\log_{10} 8 = 0.9031, then what is the value of log⁡108000+log⁡10600\log_{10} 8000 + \log_{10} 600 ?

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  2. Question 2

    CDS 2 2018

    14
    If log⁡102=0.3010\log_{10} 2 = 0.3010 and log⁡103=0.4771\log_{10} 3 = 0.4771, then the value of log⁡100(0.72)\log_{100} (0.72) is equal to

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  3. Question 3

    CDS 1 2021

    41
    What is log⁡1031.25\log_{10} 31.25 equal to?

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  4. Question 4

    CDS 1 2026

    29
    If log⁡10(80)=p\log_{10}(80) = p, log⁡10(45)=q\log_{10}(45) = q and log⁡10(216)=r\log_{10}(216) = r, then what is log⁡10(384)\log_{10}(384) equal to ?

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