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log_(7)3

log⁡73 \log _{7} 3

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Q. log⁡73 \log _{7} 3
  1. Problem Understanding: Understand the problem.\newlineWe need to find the value of the logarithm of 33 with base 77, which is written as log⁡73\log_{7}3.
  2. Logarithm Definition: Apply the definition of a logarithm.\newlineThe logarithm log⁡73\log_{7}3 asks the question: ＂To what power must we raise 77 to get 33?＂ This is not an integer value, and we cannot express 33 as a power of 77 using whole numbers or simple fractions.
  3. Solution Type: Recognize that the solution is not a simple fraction or whole number.\newlineSince 33 is not a power of 77, log⁡73\log_{7}3 will not be a whole number or a simple fraction. It is an irrational number.
  4. Final Conclusion: Conclude that the logarithm cannot be simplified further. Without a calculator or additional constraints, we cannot simplify log⁡73\log_{7}3 any further. It is an exact expression of the value we are looking for.

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