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Use a calculator to find the value to four decimal places. \( \log x=0.272 \) Question Help: Check Answer

Ask by Colon Barber. in the United States
Mar 12,2025

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Answer

\( x \approx 1.8707 \)

Solution

Calculate or simplify the expression \( \log(x)=0.272 \). Solve the equation \( \log(x)=0.272 \). Solve the equation by following steps: - step0: Solve for \(x\): \(\log_{10}{\left(x\right)}=0.272\) - step1: Find the domain: \(\log_{10}{\left(x\right)}=0.272,x>0\) - step2: Convert the logarithm into exponential form: \(x=10^{0.272}\) - step3: Evaluate the power: \(x=10^{\frac{34}{125}}\) - step4: Transform the expression: \(x=\sqrt[125]{10^{34}}\) - step5: Check if the solution is in the defined range: \(x=\sqrt[125]{10^{34}},x>0\) - step6: Find the intersection: \(x=\sqrt[125]{10^{34}}\) The value of \( x \) when \( \log x = 0.272 \) is approximately 1.870682 to four decimal places.

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To find the value of \( x \) when \( \log x = 0.272 \), you'll need to convert the logarithmic equation into its exponential form. This means that \( x = 10^{0.272} \). Using a calculator to get the value, you'll find that \( x \approx 1.8840 \) when rounded to four decimal places. This calculation comes in handy for various fields, especially in finance and science, where logarithmic scales are used to measure growth rates, pH levels, and sound intensity. Knowing how to manipulate logarithmic equations is essential for data analysis and interpreting results in these areas!

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