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x2=20242024log⁡64,x=?x^2 = 2024^{2024} \log 64, x=?

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Q. x2=20242024log⁡64,x=?x^2 = 2024^{2024} \log 64, x=?
  1. Simplify Logarithm: First, let's simplify the logarithm part of the equation. \newlinelog⁡64\log 64 is the same as log⁡264\log_2 64, which equals 66 because 26=642^6 = 64.\newlineSo, x2=20242024×6x^2 = 2024^{2024} \times 6.
  2. Calculate Huge Number: Now, let's calculate 20242024×62024^{2024} \times 6. This is a huge number and not practical to calculate directly, but since we're looking for xx and not x2x^2, we can take the square root of both sides in the next step.
  3. Take Square Root: Taking the square root of both sides gives us x=20242024×6x = \sqrt{2024^{2024} \times 6}.\newlineBut we made a mistake here; we should have simplified the equation before taking the square root.

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