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Express the given expression as an integer or as a fraction in simplest form. ln(e^((1)/(4))) Answer:

Express the given expression as an integer or as a fraction in simplest form.\newlineln⁡(e14) \ln \left(e^{\frac{1}{4}}\right) \newlineAnswer:

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Full solution

Q. Express the given expression as an integer or as a fraction in simplest form.\newlineln⁡(e14) \ln \left(e^{\frac{1}{4}}\right) \newlineAnswer:
  1. Understand Properties of Logarithms: Understand the properties of logarithms and exponents.\newlineThe natural logarithm function ln⁡(x)\ln(x) is the inverse of the exponential function exe^x. Therefore, ln⁡(ex)=x\ln(e^x) = x for any real number xx.
  2. Apply Property to Given Expression: Apply the property of logarithms to the given expression.\newlineWe have the expression ln⁡(e(1)/(4))\ln(e^{(1)/(4)}). Using the property from Step 11, we can simplify this to ln⁡(e1/4)=14\ln(e^{1/4}) = \frac{1}{4}.
  3. Check for Errors: Check for any mathematical errors.\newlineThere are no mathematical errors in the previous steps. The property of logarithms has been correctly applied.

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