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Homework Help: Finding the logarithm

  1. Oct 17, 2015 #1
    • Member warned about posting without the template.
    How do i solve Log_a (100) if Log_a (2) = 20 and Log_a (5) = 30

    I got to 2^(1/20) = 100^(1/x) and 5^(1/30) = 100^(1/x) but didnt know how to go any further.
  2. jcsd
  3. Oct 17, 2015 #2

    Ray Vickson

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    If log_a(x) means log to base "a" of x, then the two conditions you gave are inconsistent: you get two different values of "a" in the two cases.
  4. Oct 17, 2015 #3


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    Is your question "What is [itex]\log_a(100)[/itex] if [itex]\log_a(2) = 20[/itex] and [itex]\log_a(5) = 30[/itex]"?

    Well, you can get the answer from the fundamental principle of logarithms: [itex]\log_a(xy) = \log_a(x) + \log_a(y)[/itex].

    However this is a spectacularly poorly designed question, since it asserts that [itex]a^{20} = 2[/itex] and [itex]a^{30} = 5[/itex], which together require [itex]5^2 = 2^3[/itex]. This is plainly false.
  5. Oct 17, 2015 #4
    Thank you or the answers.
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