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Solve for a positive value of x. log_(3)(243)=x Answer:

Solve for a positive value of x x .\newlinelog⁡3(243)=x \log _{3}(243)=x \newlineAnswer:

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Full solution

Q. Solve for a positive value of x x .\newlinelog⁡3(243)=x \log _{3}(243)=x \newlineAnswer:
  1. Given Logarithmic Equation: We are given the logarithmic equation log⁡3(243)=x\log_3(243) = x, which means 33 raised to what power equals 243243. We need to find the value of xx.
  2. Recognize Power of 33: Recognize that 243243 is a power of 33. Specifically, 243243 is 33 raised to the 55th power, since 35=2433^5 = 243.
  3. Rewrite Equation: Since we know that 35=2433^5 = 243, we can write the equation as log⁡3(35)=x\log_3(3^5) = x.
  4. Simplify Using Property: Using the property of logarithms that log⁡b(ba)=a\log_b(b^a) = a, we can simplify the equation to 5=x5 = x.
  5. Final Value of x: Therefore, the positive value of xx that satisfies the equation is x=5x = 5.

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