precalc

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I don't understand how to do these w/o calc.
I tried to write it in a way that will make someone understand how to read it. Hope I typed it clear enough.Thanks so much for the help anyone!
How to find the exact value of logarithm:

10. log5^100 -log5^4

11. log4^8 +log4^8

12. log squareroot 100
13. log4^40 -log4^10

19. log 3^20.25 +log3^4

22. 7 log2 ^16 +log2 (1/16)
27. log 2 +log 5-log 10

31. 2 ln e^6 -ln e^5

36. log 100 + log 10,000

  • precalc -

    log5 (25)

    5^(log5(25) = 25
    but
    5^2 = 25
    so
    log5(25) = 2

  • precalc -

    you must memorize the 3 main rules of logs

    1. log (AB) = log A + log B
    2. log (A/B) = logA - logB
    3 log (A^n) = nlogA
    for any base of the log as long as the base is the same throughout the equation

    e.g.
    #22
    7log 2^16 + log (2^(1/16)) , I assumed a typo here
    = 7(16)log 2 + (1/16)log 2
    = (1793/16) log 2

    #11
    log 4^8 + log4^8
    = log (4^8 * 4^8)
    = log 4^16
    or
    = 16 log4

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