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Solve. Round your answer to the nearest thousandth.\newline7x=87^x = 8\newlinex=x = ____

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Full solution

Q. Solve. Round your answer to the nearest thousandth.\newline7x=87^x = 8\newlinex=x = ____
  1. Apply logarithm to equation: Apply the logarithm to both sides of the equation 7x=87^x = 8 to solve for x.\newlinelog(7x)=log(8)log(7^x) = log(8)
  2. Use power property of logarithms: Use the power property of logarithms to bring the exponent xx in front of the log.x⋅log⁡(7)=log⁡(8)x \cdot \log(7) = \log(8)
  3. Isolate x by dividing: Isolate x by dividing both sides of the equation by log⁡(7)\log(7).x=log⁡(8)log⁡(7)x = \frac{\log(8)}{\log(7)}
  4. Calculate x value: Calculate the value of x using a calculator.\newlinex=log⁡(8)log⁡(7)x = \frac{\log(8)}{\log(7)}\newlinex≈1.0791812460.845098040x \approx \frac{1.079181246}{0.845098040}\newlinex≈1.276x \approx 1.276

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