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Convert the exponential equation in logarithmic form.\newline10−2=110010^{-2} = \frac{1}{100}

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Full solution

Q. Convert the exponential equation in logarithmic form.\newline10−2=110010^{-2} = \frac{1}{100}
  1. Identify values: Identify bb, xx, and yy. Compare 10−2=110010^{-2} = \frac{1}{100} with by=xb^y = x. b=10b = 10 x=1100x = \frac{1}{100} y=−2y = -2
  2. Convert to logarithmic form: Convert the exponential equation to logarithmic form. Substitute b=10b=10, x=1100x=\frac{1}{100}, and y=−2y=-2 in log⁡b(x)=y\log_b(x) = y. Logarithmic equation: log⁡10(1100)=−2\log_{10}\left(\frac{1}{100}\right) = -2
  3. Find missing value: Identify the missing value in log⁡____(1100)=−2 \log_{\_\_\_\_} \left( \frac{1}{100} \right) = -2 . log⁡10(1100)=−2 \log_{10} \left( \frac{1}{100} \right) = -2 Missing value: 10 10

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