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what is log⁡(10) \log(10)

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Full solution

Q. what is log⁡(10) \log(10)
  1. Identify base logarithm: Identify the base of the logarithm in question.\newlineThe logarithm log⁡(10)\log(10) typically implies a common logarithm, which has a base of 1010. This means we are looking for the power to which the base 1010 must be raised to obtain the number 1010.
  2. Apply definition: Apply the definition of a common logarithm.\newlineBy definition, log⁡b(b)=1\log_{b}(b) = 1, because b1=bb^1 = b. Therefore, log⁡10(10)=1\log_{10}(10) = 1, since 101=1010^1 = 10.
  3. Conclude solution: Conclude the solution.\newlineSince log⁡10(10)=1\log_{10}(10) = 1, the value of log⁡(10)\log(10) is 11.

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