{ localUrl: '../page/log_inverts_exp.html', arbitalUrl: 'https://arbital.com/p/log_inverts_exp', rawJsonUrl: '../raw/3wr.json', likeableId: '2569', likeableType: 'page', myLikeValue: '0', likeCount: '3', dislikeCount: '0', likeScore: '3', individualLikes: [ 'EricBruylant', 'NateSoares', 'EricRogstad' ], pageId: 'log_inverts_exp', edit: '3', editSummary: 'The single dot is clear as mud — putting brackets around it like with log() makes it more readable.', prevEdit: '2', currentEdit: '3', wasPublished: 'true', type: 'wiki', title: 'Logarithms invert exponentials', clickbait: '', textLength: '620', alias: 'log_inverts_exp', externalUrl: '', sortChildrenBy: 'likes', hasVote: 'false', voteType: '', votesAnonymous: 'false', editCreatorId: 'JoeZeng', editCreatedAt: '2016-07-04 21:14:19', pageCreatorId: 'NateSoares', pageCreatedAt: '2016-05-28 03:22:30', seeDomainId: '0', editDomainId: 'AlexeiAndreev', submitToDomainId: '0', isAutosave: 'false', isSnapshot: 'false', isLiveEdit: 'true', isMinorEdit: 'false', indirectTeacher: 'false', todoCount: '0', isEditorComment: 'false', isApprovedComment: 'true', isResolved: 'false', snapshotText: '', anchorContext: '', anchorText: '', anchorOffset: '0', mergedInto: '', isDeleted: 'false', viewCount: '53', text: 'The function [3nd $\\log_b(\\cdot)$] inverts the function $b^{(\\cdot)}.$ In other words, $\\log_b(n) = x$ implies that $b^x = n,$ so $\\log_b(b^x)=x$ and $b^{\\log_b(n)}=n.$ (For example, $\\log_2(2^3) = 3$ and $2^{\\log_2(8)} = 8.$) Thus, logarithms give us tools for analyzing anything that grows [4ts exponentially]. If a population of bacteria grows exponentially, then logarithms can be used to answer questions about how long it will take the population to reach a certain size. If your wealth is accumulating interest, logarithms can be used to ask how long it will take until you have a certain amount of wealth. 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