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In $b^a = x$, $b$ is the base, a is the exponent and $x$ is the result of the operation. But in its logarithm counterpart, $\log_{b}(x) = a$, $b$ is still the base, and $a$ is now the result. What is $x$ called here? The exponent?

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    In $b^a=x$, $x$ (or the whole of $b^a$) is sometimes called the *power*.2010-09-07

3 Answers 3

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Argument (as you call the $x$ in any $f(x)$ argument of the function)

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Another name (that I've only ever seen when someone else asked this question) is "logarithmand".


From page 36 of The Spirit of Mathematical Analysis by Martin Ohm, translated from the German by Alexander John Ellis, 1843:

page from The Spirit of Mathematical Analysis

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    @Jonas Meyer: Please feel free to add the image; that would be neat to see. Thanks!2011-05-10
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antilogarithm (noun): a compound of Greek anti-"against" and logarithm (qq. v.). In algebra if $log_{b}(x) = y$, y is the logarithm of x, and x is said to be the antilogarithm of y.

Source: The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English, Steven Schwartzman

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    @J.M.: The point is uniformity. I'd much rather see $\rm \log_b\ exp_b\ x = x\ $ than $\rm\ \log_b\ antilog_b\ x$.2010-09-25