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Express the given expression as an integer or as a fraction in simplest form. (9^(log_(9)18+log_(9)4)) Answer:

Express the given expression as an integer or as a fraction in simplest form.\newline(9log⁡918+log⁡94) \left(9^{\log _{9} 18+\log _{9} 4}\right) \newlineAnswer:

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Full solution

Q. Express the given expression as an integer or as a fraction in simplest form.\newline(9log⁡918+log⁡94) \left(9^{\log _{9} 18+\log _{9} 4}\right) \newlineAnswer:
  1. Combine logarithms: Apply the property of logarithms that states log⁡b(m)+log⁡b(n)=log⁡b(m∗n)\log_b(m) + \log_b(n) = \log_b(m*n). So, we combine the logarithms in the exponent. (9log⁡918+log⁡94)=9log⁡9(18∗4)(9^{\log_{9}18+\log_{9}4}) = 9^{\log_{9}(18*4)}
  2. Calculate product: Calculate the product inside the logarithm.\newline18×4=7218 \times 4 = 72\newlineSo, the expression becomes 9log⁡9729^{\log_{9}72}.
  3. Simplify expression: Apply the property of logarithms that states blog⁡b(m)=mb^{\log_b(m)} = m. Since the base of the logarithm and the base of the exponent are the same (99), we can simplify the expression to just the argument of the logarithm. 9log⁡972=729^{\log_{9}72} = 72

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