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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 of a variable, solved by equating arguments or converting to exponential form.
  • Base
    The constant value that is raised to a power in exponential or logarithmic expressions.
  • 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 denoted as ln, used when the exponential base is not 10.
  • Common Logarithm
    A logarithm with base 10, denoted as log, typically 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.
  • Quotient Rule
    A logarithmic property stating that the log of a quotient equals the difference of the logs.
  • Exponential Form
    A way of expressing a logarithmic equation as a base raised to an exponent equals a value.
  • Logarithmic Form
    A way of expressing an exponential equation as a log with a specific base and argument.
  • Isolating the Exponential Expression
    The process of rearranging an equation so the exponential term stands alone on one side.
  • Argument of a Logarithm
    The value or expression inside a logarithm, which must always be positive for real solutions.
  • Like Bases
    A situation where both sides of an equation share the same base, allowing exponents to be set equal.
  • Linear Equation
    An equation of the first degree, often resulting from setting exponents or log arguments equal.
  • Undefined Logarithm
    A situation occurring when the argument of a log is zero or negative, making the expression invalid.