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Solve. Round your answer to the nearest thousandth.\newline6x=56^x = 5\newlinex=x = ____

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Q. Solve. Round your answer to the nearest thousandth.\newline6x=56^x = 5\newlinex=x = ____
  1. Apply Logarithm: 6x=56^x = 5\newlineApply the logarithm to both sides of the equation to solve for xx.\newlineextlog(6x)=extlog(5) ext{log}(6^x) = ext{log}(5)
  2. Use Power Property: log(6x)=log(5)\log(6^x) = \log(5)\newlineUse the power property of logarithms to bring the exponent xx in front of the log.\newlinexlog(6)=log(5)x \cdot \log(6) = \log(5)
  3. Isolate xx: xlog(6)=log(5)x \cdot \log(6) = \log(5)\newlineIsolate xx by dividing both sides of the equation by log(6)\log(6).\newlinex=log(5)log(6)x = \frac{\log(5)}{\log(6)}
  4. Calculate x: Calculate the value of x using a calculator.\newlinex=log(5)log(6)x = \frac{\log(5)}{\log(6)}\newlinex0.8980.778x \approx \frac{0.898}{0.778}\newlinex1.154x \approx 1.154\newlineRound the answer to the nearest thousandth.\newlinex1.154x \approx 1.154

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