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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}} .
The logarithm tells us what the exponent is! In that example the "base" is 2 and the "exponent" is 3: So the logarithm answers the question: What exponent do we need. (for one number to become another number) ? The general case is: Example: What is log10(100) ... ? 102 = 100. So an exponent of 2 is needed to make 10 into 100, and: log10(100) = 2.
Learn what logarithms are and how to evaluate them. Skip to main content If you're seeing this message, it means we're having trouble loading external resources on our website.
A logarithm is the inverse of the exponential function. Specifically, a logarithm is the power to which a number (the base) must be raised to produce a given number. For example, \log_2 64 = 6, log2 64 = 6, because 2^6 = 64. 26 = 64. In general, we have the following definition: z z is the base- x x logarithm of y y if and only if x^z = y xz = y.
Logarithm definition. When b is raised to the power of y is equal x: b y = x. Then the base b logarithm of x is equal to y: log b (x) = y. For example when: 2 4 = 16. Then. log 2 (16) = 4. Logarithm as inverse function of exponential function. The logarithmic function, y = log b (x) is the inverse function of the exponential function, x = by.
A logarithm is the inverse function of exponentiation. A logarithm tells us the power, y, that a base, b, needs to be raised to in order to equal x. This is written as: log b (x) = y. Example. Write the equivalent of 10 3 = 1000 using logarithms. Two of the most commonly used bases are base 10 (common logarithm) and base e (natural logarithm).
Logarithm is another way of writing exponent. The problems that cannot be solved using only exponents can be solved using logs. Learn more about logarithms and rules to work on them in detail.
