Question

\( \begin{array}{ll}\text { 27. Express } \ln 18=x & \text { in exponential form } \end{array} \)

Ask by O'Quinn Dickson. in the United States
Feb 03,2025

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Tutor-Verified Answer

Answer

\( e^{x} = 18 \)

Solution

To express the logarithmic equation \( \ln 18 = x \) in exponential form, you can use the relationship between logarithms and exponents. The natural logarithm \( \ln a = b \) is equivalent to the exponential form \( e^b = a \). Applying this to your equation: \[ \ln 18 = x \quad \text{is equivalent to} \quad e^{x} = 18 \] **Exponential Form:** \[ e^{x} = 18 \]

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Mind Expander

To express \( \ln 18 = x \) in exponential form, we use the definition of a natural logarithm. The equation says that \( x \) is the power to which \( e \) (approximately 2.718) must be raised to get 18. So, we can rewrite this as \( e^x = 18 \). Now you're ready to unleash the power of exponents! By converting from logarithm to exponential form, you’ve turned abstract symbols into something more tangible: \( e^x = 18 \).🎉 If you're wondering how \( e \) came into play, it's important to note that \( e \) is not just another number; it's a fundamental constant in mathematics, often referred to as Euler's number. It's so famous that it appears anywhere exponential growth is involved, from finance to population dynamics! It's like the superhero of math constants, always ready to help you express growth in the world around you! 🦸‍♂️

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