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Solve. Round your answer to the nearest thousandth.\newline9x=79^x = 7\newlinex=x = ____

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Q. Solve. Round your answer to the nearest thousandth.\newline9x=79^x = 7\newlinex=x = ____
  1. Take Logarithm: We need to solve the equation 9x=79^x = 7 for xx. To do this, we will take the logarithm of both sides of the equation.\newlinelog⁡(9x)=log⁡(7)\log(9^x) = \log(7)
  2. Simplify Left Side: Using the power property of logarithms, which states that log⁡b(Mn)=nlog⁡b(M)\log_b(M^n) = n\log_b(M), we can simplify the left side of the equation.\newlinexlog⁡(9)=log⁡(7)x\log(9) = \log(7)
  3. Isolate xx: Now we will isolate xx by dividing both sides of the equation by log⁡(9)\log(9).\newlinex=log⁡(7)log⁡(9)x = \frac{\log(7)}{\log(9)}
  4. Calculate x: We will now calculate the value of xx using a calculator.x≈log⁡(7)log⁡(9)x \approx \frac{\log(7)}{\log(9)}x≈0.84509804001425680.9542425094393249x \approx \frac{0.8450980400142568}{0.9542425094393249}x≈0.885x \approx 0.885

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