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Simplify the following: a) log_(3)(2x)+log_(3)w

Simplify the following:\newline log⁡3(2x)+log⁡3w \log _{3}(2 x)+\log _{3} w

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Full solution

Q. Simplify the following:\newline log⁡3(2x)+log⁡3w \log _{3}(2 x)+\log _{3} w
  1. Identify Property: We have log⁡3(2x)+log⁡3(w)\log_3(2x) + \log_3(w). \newlineAccording to logarithmic properties, the sum of logs with the same base can be combined into a single log that multiplies the arguments.
  2. Apply Product Property: Apply the product property: log⁡b(a)+log⁡b(b)=log⁡b(ab)\log_b(a) + \log_b(b) = \log_b(ab) \newlineCombine the logs: log⁡3(2x)+log⁡3(w)=log⁡3(2x⋅w)\log_3(2x) + \log_3(w) = \log_3(2x \cdot w).

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