Question:

Please answer this one! How do i solve 2=3^(0.6934t). ?

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I think it has something to do with logs but i do not remember, please share knowledge!

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  1. take the log of both sides

    log2=log(3^.6934t)

    use a property of logs

    log2=.6934tlog3

    t=log2/(.6934log3)

    plug that into a calculator

    btw that log can be any base. ln, (e), log, (10), or log_n where n is any other non-0 non-1 positive integer


  2. Remember:

    log a^n = n log a

    log ab = log a+log b

    log a/b = log a-log b


  3. log 2 = 0.6934 t (log 3)

    0.6934 t = log 2 / log 3

    t = [ log 2 / log 3 ] / 0.6934

    t = 0.910---------(any log base may be used)

  4. Use logarithms:

    2 = 3^(0.6934t)

    log 2 = log 3^(0.6934t)

    Logarithmic laws say you can bring out the 0.6934t in front of the log 3:

    log 2 = 0.6934t * log 3

    Divide by log 3:

    log 2 / log 3 = 0.6934t

    Divide by 0.6934:

    (log 2 / log 3) / 0.6934 = t

    t ≈ 0.9099

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