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If two quantities are equal, are their logarithms also equal? Consider the questions below.

  1. Is it true that is equal to ? Is this a special case, or is equal to for any values of and ?

    Try a few other combinations of and .

  2. Is log equal to log ? How can you be sure?

    Simplify the exponential expressions first.

  3. Are the equations and equivalent? Justify your answer.

    What solutions satisfy each equation?

  4. Is the equation equivalent to the equation ? How can you be sure?

    See part (c).