In 1815, Peter Roget invented the log log slide rule, which included a scale displaying the logarithm of the logarithm. This allowed the user to directly perform calculations involving roots and exponents. This was especially useful for fractional powers.
ɪ n WORD_BOUNDARY w ʌ n WORD_BOUNDARY θ aʊ z ə n d WORD_BOUNDARY eɪ t h ʌ n d ɹ ɪ d WORD_BOUNDARY f ɪ f t iː n WORD_BOUNDARY p iː t ə ɹ WORD_BOUNDARY ɹ ɑ d̠ʒ ɪ t WORD_BOUNDARY ɪ n v ɛ n t ɪ d WORD_BOUNDARY ð ə WORD_BOUNDARY l ɔ ɡ WORD_BOUNDARY l ɔ ɡ WORD_BOUNDARY s l aɪ d WORD_BOUNDARY ɹ uː l WORD_BOUNDARY w ɪ t̠ʃ WORD_BOUNDARY ɪ ŋ k l uː d ɪ d WORD_BOUNDARY ʌ WORD_BOUNDARY s k eɪ l WORD_BOUNDARY d ɪ s p l eɪ ɪ ŋ WORD_BOUNDARY ð ə WORD_BOUNDARY l ɑ ɡ ə ɹ ɹ ɪ θ ə m WORD_BOUNDARY ʌ v ð ə WORD_BOUNDARY l ɑ ɡ ə ɹ ɹ ɪ θ ə m WORD_BOUNDARY ð ɪ s WORD_BOUNDARY ʌ l aʊ d WORD_BOUNDARY ð ə WORD_BOUNDARY j uː z ə ɹ WORD_BOUNDARY t ə WORD_BOUNDARY d ɪ ɹ ɛ k t l i WORD_BOUNDARY p ə ɹ f ɔ ɹ m WORD_BOUNDARY k æ l k j ʊ l eɪ ʃ ə n z WORD_BOUNDARY ɪ n v ɑ l v ɪ ŋ WORD_BOUNDARY ɹ uː t s WORD_BOUNDARY æ n d WORD_BOUNDARY ɛ k s p oʊ n ə n t s WORD_BOUNDARY ð ɪ s WORD_BOUNDARY w ʌ z WORD_BOUNDARY ɪ s p ɛ ʃ ə l i WORD_BOUNDARY j uː s f ə l WORD_BOUNDARY f ɔ ɹ WORD_BOUNDARY f ɹ æ k ʃ ə n ə l WORD_BOUNDARY p aʊ ə ɹ z WORD_BOUNDARY