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log_(10)10,000=

log⁡1010,000= \log _{10} 10,000=

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Q. log⁡1010,000= \log _{10} 10,000=
  1. Identify bb, xx, and yy: Identify bb, xx, and yy.\newlineCompare log⁡(10)10,000\log_{(10)} 10,000 with log⁡(b)x=y\log_{(b)}x = y.\newlineb=10b = 10\newlinex=10,000x = 10,000\newlinexx00
  2. Understand the definition of a logarithm: Understand the definition of a logarithm.\newlineThe logarithm log⁡bx=y\log_{b}x = y means that bb raised to the power yy equals xx.\newlineSo, log⁡10x=y\log_{10}x = y means 10y=x10^y = x.
  3. Apply the definition to the given logarithm: Apply the definition to the given logarithm.\newlineSince log⁡1010,000\log_{10} 10,000 is given, we want to find yy such that 10y=10,00010^y = 10,000.\newlineWe know that 104=10,00010^4 = 10,000.\newlineTherefore, y=4y = 4.
  4. Write the exponential form of the logarithmic equation: Write the exponential form of the logarithmic equation.\newlineSince we found that y=4y = 4, the exponential form is 104=10,00010^4 = 10,000.

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