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log_(2)(1234)~~

log⁡2(1234)≈ \log _{2}(1234) \approx

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Full solution

Q. log⁡2(1234)≈ \log _{2}(1234) \approx
  1. Identify Power of 22: Identify that we need to express 12341234 as a power of 22. Since 12341234 is not a power of 22, we'll use a calculator to find the approximate value.
  2. Change of Base Formula: Use the change of base formula: log⁡2(1234)=log⁡(1234)log⁡(2)\log_2(1234) = \frac{\log(1234)}{\log(2)}.
  3. Calculate Logs: Calculate log⁡(1234)\log(1234) and log⁡(2)\log(2) using a calculator.\newlinelog⁡(1234)≈3.0913\log(1234) \approx 3.0913, log⁡(2)≈0.3010\log(2) \approx 0.3010.
  4. Divide Logs: Divide log⁡(1234)\log(1234) by log⁡(2)\log(2) to find the value of log⁡2(1234)\log_2(1234).\newlinelog⁡2(1234)≈3.09130.3010.\log_2(1234) \approx \frac{3.0913}{0.3010}.
  5. Perform Division: Perform the division to get the approximate value. log⁡2(1234)≈10.27\log_2(1234) \approx 10.27.

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