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Logarithm help, Log(base 5)25X?

The answer is 2+log(base5)X. Can somebody explain this please and if they know a website that explains this that would be helpful too, thanks.

Update:

Okay nevermind I figured it out, thanks for looking though. IF there is still any good logarithm help sites, could you please put them down, it would be much appreciated.

5 Answers

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  • 1 decade ago
    Favorite Answer

    log[5]25x

    =>log[5]25 + log[5] x (since log ab = log a + logb)

    =>log[5]5^2 + log[5]x

    =>2log[5]5 + log[5]x (since loga^b = b log a)

    =>2 + log[5]x (since log of any number to the base of same

    number = 1)

  • Como
    Lv 7
    1 decade ago

    Let log be understood as log to base 5 :-

    log (25 X) = log 25 + log X

    log (25X) = 2 + log X

  • Joe L
    Lv 5
    1 decade ago

    Remember that when you multiply numbers by one another, you ADD their logs.

    For example, Log (base 2) 4 = 2

    Log (base 2) 8 = 3

    Log (base 2)4X8 = Log(base 2)32 = 5

    So you can "take your logs apart" and express them as follows:

    Log(base 5)25X = Log(base 5) X + Log(base 5) 25

    But

    Log(base 5)25 = 2

    So the answer is

    2 + Log(base 5)X

  • norman
    Lv 7
    1 decade ago

    use the law of log addition

    Log nm = log m + log n

    log25x = log 25 + log x

    log (base 5)25 = log (base 5) 5^2

    use the law of log muliplication

    Log m^n = n log m

    log(base 5)5^2 = 2 log(base 5)5

    log(base 5)5 = 1 so that is your ans.

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  • Anonymous
    4 years ago

    i think of maths is all approximately loving.....if u prepare and get alongside with it each and every answer is nearly a puzzle it incredibly is hard yet while u conquer it u could be the happiest guy in the worldwide....

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