The Labyrinth of Logarithmic Mysteries

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 In a mythical labyrinth, a treasure chest is locked behind a door with a log-based code. The code is the solution to the following logarithmic equation:

log⁡2(�)+log⁡2(�−4)=3. To unlock the chest and claim the treasure, you must find the value of � that satisfies this equation. Remember, logarithmic properties might be helpful in solving this equation.

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  1. AnonymousDecember 4, 2023 at 11:05 PM

    Using Logarithmic Properties:

    Combine the logarithms: log2(x) + log2(x-4) becomes log2(x * (x-4)).
    Setting up the Equation:

    The equation is now log2(x * (x-4)) = 3.
    Convert the logarithmic equation into an exponential equation: 2^3 = x * (x-4).
    Solving the Quadratic Equation:

    2^3 is 8, so the equation is 8 = x * (x-4).
    Simplify this to x^2 - 4x - 8 = 0.
    Solve this quadratic equation to find the value of x.

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