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Solve. Round your answer to the nearest thousandth.\newline 7=8x 7 = 8^x \newline x= x = ____

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Q. Solve. Round your answer to the nearest thousandth.\newline 7=8x 7 = 8^x \newline x= x = ____
  1. Write Equation: Write down the equation.\newlineWe have the equation 7=8x7 = 8^x.
  2. Apply Logarithm: Apply the logarithm to both sides of the equation.\newlineTaking the logarithm of both sides gives us log⁡(7)=log⁡(8x)\log(7) = \log(8^x).
  3. Use Power Property: Use the power property of logarithms.\newlineThe power property of logarithms states that log⁡(ab)=b⋅log⁡(a)\log(a^b) = b \cdot \log(a). Applying this to our equation gives us log⁡(7)=x⋅log⁡(8)\log(7) = x \cdot \log(8).
  4. Isolate Variable x: Isolate the variable xx.\ To solve for xx, we divide both sides by log⁡(8)\log(8), which gives us x=log⁡(7)log⁡(8)x = \frac{\log(7)}{\log(8)}.
  5. Calculate with Calculator: Calculate the value of xx using a calculator.\newlineUsing a calculator, we find that log⁡(7)≈0.845098040\log(7) \approx 0.845098040 and log⁡(8)≈0.903089987\log(8) \approx 0.903089987. Therefore, x≈0.8450980400.903089987x \approx \frac{0.845098040}{0.903089987}.
  6. Perform Division: Perform the division to find the value of xx.\newlineAfter dividing, we get x≈0.935507576x \approx 0.935507576.
  7. Round to Nearest Thousandth: Round the answer to the nearest thousandth.\newlineRounding 0.9355075760.935507576 to the nearest thousandth gives us x≈0.936x \approx 0.936.

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