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

Express the given expression without logs, in simplest form. Assume all variables represent positive values.\newlinelog⁡3(33y3) \log _{3}\left(3^{3 y^{3}}\right) \newlineAnswer:

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Q. Express the given expression without logs, in simplest form. Assume all variables represent positive values.\newlinelog⁡3(33y3) \log _{3}\left(3^{3 y^{3}}\right) \newlineAnswer:
  1. Identify Property: Identify the property of logarithms that allows us to simplify the expression log⁡3(33y3)\log_{3}(3^{3y^{3}}).\newlineThe expression involves a logarithm with the same base as the exponent of the argument. According to the inverse property of logarithms, log⁡b(bx)=x\log_b(b^x) = x.
  2. Apply Inverse Property: Apply the inverse property of logarithms to simplify the expression.\newlineSince the base of the logarithm and the base of the exponent are the same (both are 33), we can simplify the expression to just the exponent.\newlineTherefore, log⁡3(33y3)\log_{3}(3^{3y^{3}}) simplifies to 3y33y^{3}.

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