The New York Times Crossword · 51-Across · 9 letters

Inverse of an exponential function The New York Times Crossword clue

Editorially reviewed October 4, 2026

Answer · 9 letters

LOGARITHM

LOGARITHM is the nine-letter fill. If 2 raised to an exponent gives 32, a base-2 logarithm reverses the question and returns that exponent: log base 2 of 32 is 5 because 2 to the fifth power is 32. More generally, the inverse of y = b to the x is x = log base b of y, for positive b other than 1.

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Reverse an exponent question

An exponential function starts with a base and exponent and produces a number. A logarithm starts with the base and result and returns the exponent. For example, 2 to the fifth power is 32, so the base-2 logarithm of 32 is 5. That reversal is what 'inverse' means here.

Use the nine squares and the unspecified base

LOG is the short notation, but it fills only three squares; LOGARITHM fills all nine. The clue does not give a base, so it asks for the general mathematical name, not a particular value such as log base 2 of 32. For a positive base other than 1, the logarithmic function is the inverse of the exponential function with that same base.

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Where this clue appeared

51-Across in The New York Times Crossword puzzle for August 29, 2026.

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