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Solve for xx. \newline7=9x7 = 9^x\newlineRound your answer to the nearest thousandth.

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Q. Solve for xx. \newline7=9x7 = 9^x\newlineRound your answer to the nearest thousandth.
  1. Apply Logarithm: To solve the equation 7=9x7 = 9^x for xx, we will take the logarithm of both sides of the equation. This is because logarithms allow us to solve for the exponent in an exponential equation.\newlineCalculation: Apply the logarithm to both sides.\newlinelog⁡(7)=log⁡(9x)\log(7) = \log(9^x)
  2. Use Power Property: Next, we use the power property of logarithms, which states that log⁡b(Mn)=n⋅log⁡b(M)\log_b(M^n) = n \cdot \log_b(M), to simplify the right side of the equation.\newlineCalculation: Simplify the equation using the power property.\newlinelog⁡(7)=x⋅log⁡(9)\log(7) = x \cdot \log(9)
  3. Isolate xx: Now, we isolate xx by dividing both sides of the equation by log⁡(9)\log(9).\newlineCalculation: Divide both sides by log⁡(9)\log(9) to solve for xx.\newlinex=log⁡(7)log⁡(9)x = \frac{\log(7)}{\log(9)}
  4. Calculate Value: Finally, we calculate the value of xx using a calculator and round the answer to the nearest thousandth.\newlineCalculation: Use a calculator to find the value of xx.\newlinex=log⁡(7)log⁡(9)x = \frac{\log(7)}{\log(9)}\newlinex≈0.8850.954x \approx \frac{0.885}{0.954}\newlinex≈0.927x \approx 0.927

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