Algebra

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How come log5 25^4 reduces to 4 log5 25
then 4 times 2
then finally eight?

  • Algebra -

    log x^n = n log x
    so
    log5 25^4 = 4 log5 25

    25 = 5^2
    so
    4 log5 25 = 4 log5 5^2
    = 4*2 log5 5

    5^(log5 x) = x
    5^(log5 5) = 5
    so
    log5 5 = 1
    SO
    4*2*1 = 8

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