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Solve for a positive value of x. log_(9)(x)=3 Answer:

Solve for a positive value of x x .\newlinelog⁡9(x)=3 \log _{9}(x)=3 \newlineAnswer:

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Full solution

Q. Solve for a positive value of x x .\newlinelog⁡9(x)=3 \log _{9}(x)=3 \newlineAnswer:
  1. Identify Property: Identify the property of logarithms to solve for xx. The equation log⁡9(x)=3\log_{9}(x) = 3 can be rewritten using the definition of logarithms, which states that if log⁡b(a)=c\log_{b}(a) = c, then bc=ab^{c} = a.
  2. Rewrite Equation: Rewrite the logarithmic equation in exponential form.\newlineUsing the property from Step 11, we can express log⁡9(x)=3\log_{9}(x) = 3 as 93=x9^{3} = x.
  3. Calculate Value: Calculate the value of 939^3. \newline93=9×9×9=81×9=7299^3 = 9 \times 9 \times 9 = 81 \times 9 = 729.
  4. Conclude Solution: Conclude the value of xx.\newlineSince 93=7299^3 = 729, we have x=729x = 729, which is the positive value we were solving for.

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