Exponents, roots, and logarithms are three operations that represent the same mathematical relationship, differing only in which variable is being solved for: exponentiation finds the result when base and exponent are known, roots find the base when result and exponent are known, and logarithms find the exponent when base and result are known. For example, 10³ = 1,000, the fourth root of 81 is 3, and log base 3 of 81 is 4 all describe the same relationship.
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Exponents / Roots / Logs - Same triangle.Added:
Exponents, roots, and logs, same triangle. 10 cubed equals 1,000. 10 is the base, three is the exponent, 1,000 is the result. Exponent on top, base bottom left, result bottom right. Cover the result, exponentiation. Cover the base, that's a root. Cover the exponent, that's a log. 3 to the fourth is 81. Log base three of 81, four. Fourth root of 81, three. Same three numbers, same triangle.
Notice the log always gives you back the exponent. That's literally what it does.
Three operations, one relationship, which number is missing?
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