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Write the expression below as a single logarithm in simplest form. log_(b)4-log_(b)4 Answer: log_(b)(◻)

Write the expression below as a single logarithm in simplest form.\newlinelog⁡b4−log⁡b4 \log _{b} 4-\log _{b} 4 \newlineAnswer: log⁡b(□) \log _{b}(\square)

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Quotient property of logarithmsright chevron icon

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Q. Write the expression below as a single logarithm in simplest form.\newlinelog⁡b4−log⁡b4 \log _{b} 4-\log _{b} 4 \newlineAnswer: log⁡b(□) \log _{b}(\square)
  1. Identify Property: Identify the property used to combine the logarithms.\newlineThe expression log⁡b4−log⁡b4\log_{b}4 - \log_{b}4 involves the subtraction of two logarithms with the same base and the same argument.\newlineThe property that applies here is that the logarithm of any number minus itself is 00.
  2. Apply Property: Apply the property to combine the logarithms.\newlineSince log⁡b4\log_{b}4 and log⁡b4\log_{b}4 are the same, their difference is zero.\newlinelog⁡b4−log⁡b4=0\log_{b}4 - \log_{b}4 = 0
  3. Write Single Logarithm: Write the expression as a single logarithm.\newlineThe expression 00 can be written as log⁡b1\log_{b}1 because the logarithm of 11 to any base is 00.\newlineTherefore, log⁡b4−log⁡b4=log⁡b1\log_{b}4 - \log_{b}4 = \log_{b}1

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