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log_(10)1,000=

log⁡101,000= \log _{10} 1,000=

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Q. log⁡101,000= \log _{10} 1,000=
  1. Identify base, number, exponent: Identify the base bb, the number xx, and the exponent yy that the logarithm is equal to.\newlineIn the logarithmic equation log⁡101000\log_{10}1000, the base bb is 1010 and the number xx is 10001000. We need to find the exponent yy such that 10y=100010^y = 1000.
  2. Recognize power of 1010: Recognize that 1,0001,000 is a power of 1010. Specifically, 1,0001,000 is 10310^3 because 10×10×10=1,00010 \times 10 \times 10 = 1,000.
  3. Write exponential form: Write the exponential form of the logarithmic equation. Since we know that 103=1,00010^3 = 1,000, the logarithmic equation log⁡101,000\log_{10}1,000 is equal to 33.
  4. Confirm equivalence: Confirm that the exponential form matches the original logarithmic equation. The logarithmic equation log⁡101000=3\log_{10}1000 = 3 is equivalent to the exponential equation 103=1,00010^3 = 1,000.

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