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Solving Exponential and Logarithmic Equations definitions

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  • Exponential Equation
    An equation where the variable appears in the exponent, often requiring base rewriting or logarithms to solve.
  • Logarithmic Equation
    An equation involving a logarithm with the variable inside, typically solved by converting to exponential form or using log properties.
  • Base
    The constant value that is raised to a power in exponential or logarithmic expressions, crucial for rewriting and solving equations.
  • Exponent
    The power to which a base is raised, often containing the variable to be solved in exponential equations.
  • Natural Logarithm
    A logarithm with base e, commonly used when the exponential base is not 10, denoted as ln.
  • Common Logarithm
    A logarithm with base 10, typically written as log, used when the exponential base is 10.
  • Power Rule
    A logarithmic property allowing exponents inside a log to be moved in front as a multiplier, aiding in isolating variables.
  • Quotient Rule
    A logarithmic property stating that the log of a quotient equals the difference of the logs, useful for condensing expressions.
  • Isolated Exponential Expression
    An exponential term arranged alone on one side of an equation, a key step before applying logarithms.
  • Exponential Form
    A mathematical expression where a base is raised to an exponent, often used to rewrite logarithmic equations for solving.
  • Logarithmic Form
    An expression representing the exponent needed to obtain a number from a given base, used to solve exponential equations.
  • Linear Equation
    A simplified equation with the variable to the first power, often resulting from solving exponential or logarithmic equations.
  • Undefined Logarithm
    A situation where the argument of a logarithm is negative or zero, making the expression invalid and the solution extraneous.
  • Like Bases
    Identical bases on both sides of an equation, allowing exponents to be set equal for straightforward solving.
  • Approximate Solution
    A decimal value for a variable, typically found using a calculator after applying logarithms or other properties.