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9x=3339^x=333\newlineFind XX

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Full solution

Q. 9x=3339^x=333\newlineFind XX
  1. Calculate logarithm to isolate xx: Calculate the logarithm of both sides to isolate xx. Using log base 1010, log⁡(9x)=log⁡(333)\log(9^x) = \log(333). Using the power rule of logarithms, x⋅log⁡(9)=log⁡(333)x \cdot \log(9) = \log(333).
  2. Calculate logs using calculator: Calculate log⁡(9)\log(9) and log⁡(333)\log(333) using a calculator.\newlinelog⁡(9)≈0.9542\log(9) \approx 0.9542, log⁡(333)≈2.5224\log(333) \approx 2.5224.
  3. Solve for x by dividing logs: Solve for x by dividing the logs.\newlinex=log⁡(333)log⁡(9)x = \frac{\log(333)}{\log(9)}.\newlinex≈2.52240.9542≈2.64x \approx \frac{2.5224}{0.9542} \approx 2.64.

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