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Express the given expression without logs, in simplest form. Assume all variables represent positive values. (3^(log_(3)(7sqrtz))) Answer:

Express the given expression without logs, in simplest form. Assume all variables represent positive values.\newline(3log⁡3(7z)) \left(3^{\log _{3}(7 \sqrt{z})}\right) \newlineAnswer:

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Properties of logarithms: mixed reviewright chevron icon

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Q. Express the given expression without logs, in simplest form. Assume all variables represent positive values.\newline(3log⁡3(7z)) \left(3^{\log _{3}(7 \sqrt{z})}\right) \newlineAnswer:
  1. Recognize Property: Recognize the property of logarithms that will be used to simplify the expression.\newlineThe property that will be used is the inverse property of logarithms and exponents, which states that for any base bb, blog⁡b(x)=xb^{\log_b(x)} = x.
  2. Apply Inverse Property: Apply the inverse property of logarithms to the expression.\newlineUsing the inverse property, we can simplify 3log⁡3(7z)3^{\log_{3}(7\sqrt{z})} by recognizing that the base of the exponent and the base of the logarithm are the same (base 33).\newlineTherefore, 3log⁡3(7z)3^{\log_{3}(7\sqrt{z})} simplifies to 7z7\sqrt{z}.

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