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solve the equation

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Solve the equation
log[14](x+49) - log[196] x=1

  • solve the equation - ,

    Given
    log14x+49 - log196x = 1

    We will use a lemma that
    logax=log=x²

    Since 196=14², we write above as
    log14x+49 - log14²x = 1
    Then
    log14²(x+49)² - log14²x = 1
    Rewrite using laws of logarithm:
    log14²(x+49)²/x = 1
    Using the alternate form from the definition of logarithms,
    (x+49)^2/x = 14²
    Transpose and solve for x to get
    (x-49)²=0, or
    x=49

  • solve the equation - typo - ,

    We will use a lemma that states:
    logax = log

    The proof of the lemma is left to you as an exercise, if it was not already covered in your course.

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