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A logarithmic equation is an equation in which one or more of the unknowns appear within a logarithmic function. In other words, these equations involve logarithms of unknown variables and can be resolved using logarithm properties and algebraic techniques.
4 Αυγ 2024 · Logarithm is a mathematical function that represents the exponent to which a fixed number, known as the base, must be raised to produce a given number. In other words, it is the inverse operation of exponentiation.
The logarithmic function is the inverse function of exponentiation. Visit BYJU'S to learn the formulas, important properties and rules used in logarithms with examples.
Logarithmic Equations. We have already seen that every logarithmic equation logb(x)= y l o g b (x) = y is equal to the exponential equation by = x b y = x. We can use this fact, along with the rules of logarithms, to solve logarithmic equations where the argument is an algebraic expression.
The logarithm is denoted "log b x" (pronounced as "the logarithm of x to base b", "the base-b logarithm of x", or most commonly "the log, base b, of x "). An equivalent and more succinct definition is that the function log b is the inverse function to the function x ↦ b x {\displaystyle x\mapsto b^{x}} .
28 Μαΐ 2024 · Restriction on the Variable. For Base. The base ‘b’ of a logarithm is always a positive real number (b > 0) and does not equal 1 (b ≠ 1). For negative bases, logarithm leads to complex results. Now, let us assume the base is 1, and the equation is: log 1 7 = x ⇒ 1 x = 7. Since 1 raised to any power yields 1, 1 x = 7 is false.
13 Δεκ 2023 · Definition of the logarithmic function: For \(x>0\), \(b>0\), \(b≠1\), \(y={\log}_b(x)\) if and only if \(b^y=x\). Definition of the common logarithm: For \(x>0\), \(y=\log(x)\) if and only if \({10}^y=x\). Definition of the natural logarithm: For \(x>0\), \(y=\ln(x)\) if and only if \(e^y=x\).
