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Solve. Write your answer as an integer or a fraction in simplest form. \newline5=3x5 = 3^x \newline x=x= ______

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Full solution

Q. Solve. Write your answer as an integer or a fraction in simplest form. \newline5=3x5 = 3^x \newline x=x= ______
  1. Recognize the equation: Recognize the equation 5=3x5 = 3^x is an exponential equation where we need to find the value of xx.
  2. Use logarithms: Since 55 is not a power of 33, we can't find an integer value for xx. We'll have to use logarithms.
  3. Take logarithm: Take the logarithm of both sides of the equation to get log⁡(5)=x⋅log⁡(3)\log(5) = x \cdot \log(3).
  4. Divide to isolate xx: Divide both sides by log⁡(3)\log(3) to isolate xx, so x=log⁡(5)log⁡(3)x = \frac{\log(5)}{\log(3)}.
  5. Calculate with calculator: Use a calculator to find the values of log⁡(5)\log(5) and log⁡(3)\log(3).
  6. Find xx value: Calculate x=log⁡(5)log⁡(3)x = \frac{\log(5)}{\log(3)} which is approximately 1.464971.46497.

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