Logarithm Help?

Question: If log[b]4=k, then log[b]16=?

Answer: 2k

I had it last night but know I forgot how the algorithm for this problem and I would appreciate any sort of help.

2 Answers

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  • 1 month ago
    Favorite Answer

    Log[b](4) = k → you know that: Log[a](x) = Ln(x) / Ln(a) ← where a is the base

    Ln(4) / Ln(b) = k → you multiply by 2 both sides

    2.Ln(4) / Ln(b) = 2k → you know that: x.Ln(a) = Ln(a^x)

    Ln(16) / Ln(b) = 2k

    Log[b](16) = 2k

  • 1 month ago

    log_b(4) = k

    You want to find out what log_b(16) is.

    Let's call that x:

    x = log_b(16)

    So you want a value for x in terms of k.

    Note that 16 is a power of 4, so:

    x = log_b(4²)

    We can pull the exponent out of the log to get:

    x = 2 log_b(4)

    And finally, substitute the variable k for the log expression:

    x = 2k

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