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Portal Reloaded is a single-player mod for Portal 2 created by Jannis Brinkmann and was released on April 19, 2021, exactly 10 years after the release of Portal 2. [274] The mod gives players the ability to fire a third portal, the "time portal", to travel between the present and future versions of each test chamber.
The graph of the logarithm base 2 crosses the x-axis at x = 1 and passes through the points (2, 1), (4, 2), and (8, 3), depicting, e.g., log 2 (8) = 3 and 2 3 = 8. The graph gets arbitrarily close to the y-axis, but does not meet it. Addition, multiplication, and exponentiation are three of the most fundamental arithmetic operations.
Like the Portal series, Portal Reloaded is a puzzle-platform game played from the first-person perspective in which the player must solve puzzles in "test chambers". [1] [2] [3] The player is equipped with the portal gun, allowing them to create two ends of a portal, colored orange and blue, that connect disparate areas in three-dimensional ...
For example, two numbers can be multiplied just by using a logarithm table and adding. These are often known as logarithmic properties, which are documented in the table below. [2] The first three operations below assume that x = b c and/or y = b d, so that log b (x) = c and log b (y) = d. Derivations also use the log definitions x = b log b (x ...
It can also be useful when applied to functions raised to the power of variables or functions. Logarithmic differentiation relies on the chain rule as well as properties of logarithms (in particular, the natural logarithm , or the logarithm to the base e ) to transform products into sums and divisions into subtractions.
Exponential functions with bases 2 and 1/2. The exponential function is a mathematical function denoted by () = or (where the argument x is written as an exponent).Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.
Many properties of the real logarithm also apply to the logarithmic derivative, even when the function does not take values in the positive reals. For example, since the logarithm of a product is the sum of the logarithms of the factors, we have () ′ = ( + ) ′ = () ′ + () ′.
Historically, it was known as logarithmus decimalis [2] or logarithmus decadis. [3] It is indicated by log(x), [4] log 10 (x), [5] or sometimes Log(x) with a capital L; [note 1] on calculators, it is printed as "log", but mathematicians usually mean natural logarithm (logarithm