Here are the essential concepts you must grasp in order to answer the question correctly.
Natural Logarithm
The natural logarithm, denoted as ln, is the logarithm to the base e, where e is approximately 2.71828. It is a fundamental concept in algebra and calculus, often used to solve equations involving exponential growth or decay. Understanding how to manipulate natural logarithms is essential for solving equations like the one presented.
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Exponential Equations
Exponential equations are equations in which variables appear as exponents. To solve these equations, one often uses logarithmic properties to isolate the variable. In the given equation, 5 ln x = 10, recognizing that ln x can be rewritten in exponential form is crucial for finding the solution.
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Isolating the Variable
Isolating the variable is a key algebraic technique used to solve equations. This involves rearranging the equation to get the variable on one side and all other terms on the opposite side. In the context of the given equation, this means manipulating the equation to express x in terms of known quantities, which is necessary for finding the exact solution.
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