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Write the expression below as a single logarithm in simplest form. log_(b)3+log_(b)2 Answer: log_(b)(◻)

Write the expression below as a single logarithm in simplest form.\newlinelog⁡b3+log⁡b2 \log _{b} 3+\log _{b} 2 \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⁡b3+log⁡b2 \log _{b} 3+\log _{b} 2 \newlineAnswer: log⁡b(□) \log _{b}(\square)
  1. Identify Property: Identify the property used to combine log⁡b(3)\log_b(3) and log⁡b(2)\log_b(2). When adding two logarithms with the same base, we can use the product property of logarithms.\newlineProduct Property: log⁡b(M)+log⁡b(N)=log⁡b(M×N)\log_b (M) + \log_b (N) = \log_b (M \times N)
  2. Apply Property: Apply the product property to combine log⁡b(3)\log_b(3) and log⁡b(2)\log_b(2).\newlineUsing the product property, we combine the two logarithms:\newlinelog⁡b(3)+log⁡b(2)=log⁡b(3×2)\log_b(3) + \log_b(2) = \log_b(3 \times 2)
  3. Perform Multiplication: Perform the multiplication inside the logarithm.\newlineMultiply the constants inside the logarithm:\newlinelog⁡b(3×2)=log⁡b(6)\log_b(3 \times 2) = \log_b(6)
  4. Check Simplified Form: Check if the expression is in the simplest form.\newlineThe expression log⁡b(6)\log_b(6) is already in the simplest form because it is a single logarithm with a distinct constant inside.

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