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15 June, 20:19

If log (m/n) = 4 and log (p/n) = 5 what is the relationship between m and p? p=100m p=10m p=0.1m m=10p

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  1. 15 June, 20:31
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    Log (A/B) = logA - logB By law of logarithm

    log (m/n) = 4

    logm - logn = 4 ... (a)

    log (p/n) = 5

    logp - logn = 5 ... (b)

    Equation (a) minus (b)

    logm - logp - logn - (-logn) = 5 - 4

    logm - logp - logn + logn = 1

    logm - logp = 1

    log (m/p) = 1

    log₁₀ (m/p) = 1.

    All the while the logarithm has been to base 10. Once a base is not written in logarithm, it is taken to be base 10.

    log₁₀ (m/p) = 1

    (m/p) = 10¹ conversion from logarithm to indices

    m/p = 10

    m = 10p
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