{ localUrl: '../page/425.html', arbitalUrl: 'https://arbital.com/p/425', rawJsonUrl: '../raw/425.json', likeableId: '0', likeableType: 'page', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], pageId: '425', edit: '1', editSummary: '', prevEdit: '0', currentEdit: '1', wasPublished: 'true', type: 'comment', title: '"I think you may need to spe..."', clickbait: '', textLength: '143', alias: '425', externalUrl: '', sortChildrenBy: 'recentFirst', hasVote: 'false', voteType: '', votesAnonymous: 'false', editCreatorId: 'EricRogstad', editCreatedAt: '2016-06-07 17:56:09', pageCreatorId: 'EricRogstad', pageCreatedAt: '2016-06-07 17:56:09', seeDomainId: '0', editDomainId: 'AlexeiAndreev', submitToDomainId: '0', isAutosave: 'false', isSnapshot: 'false', isLiveEdit: 'true', isMinorEdit: 'false', indirectTeacher: 'false', todoCount: '0', isEditorComment: 'true', isApprovedComment: 'true', isResolved: 'true', snapshotText: '', anchorContext: 'Specifically, if a number $x$ is $n$ digits long \\(in decimal\\_notation\\), then its logarithm \\(base 10\\) is between $n-1$ and $n$\\. This follows directly from the definition of the logarithm: $\\log_{10}(x)$ is the number of times you have to multiply 1 by 10 to get $x;$ and each new digit lets you write down ten times as many numbers\\. Thus, the number of digits you need to write $x$ is close to the number of times you have to multiply 1 by 10 to get $x$\\. The only difference is that, when using digits to write numbers down, you only get to use whole digits, whereas when computing logs, you can multiply 1 by 10 fractionally\\-many times\\.', anchorText: 'lets you write down ten times as many number', anchorOffset: '291', mergedInto: '', isDeleted: 'false', viewCount: '953', text: 'I think you may need to spell out this 10 times as many numbers part. This is a large unexplained step in explaining why the log is the length.', metaText: '', isTextLoaded: 'true', isSubscribedToDiscussion: 'false', isSubscribedToUser: 'false', isSubscribedAsMaintainer: 'false', discussionSubscriberCount: '1', maintainerCount: '1', userSubscriberCount: '0', lastVisit: '', hasDraft: 'false', votes: [], voteSummary: 'null', muVoteSummary: '0', voteScaling: '0', currentUserVote: '-2', voteCount: '0', lockedVoteType: '', maxEditEver: '0', redLinkCount: '0', lockedBy: '', lockedUntil: '', nextPageId: '', prevPageId: '', usedAsMastery: 'false', proposalEditNum: '0', permissions: { edit: { has: 'false', reason: 'You don't have domain permission to edit this page' }, proposeEdit: { has: 'true', reason: '' }, delete: { has: 'false', reason: 'You don't have domain permission to delete this page' }, comment: { has: 'false', reason: 'You can't comment in this domain because you are not a member' }, proposeComment: { has: 'true', reason: '' } }, summaries: {}, creatorIds: [ 'EricRogstad' ], childIds: [], parentIds: [ 'log_as_length' ], commentIds: [], questionIds: [], tagIds: [], relatedIds: [], markIds: [], explanations: [], learnMore: [], requirements: [], subjects: [], lenses: [], lensParentId: '', pathPages: [], learnMoreTaughtMap: {}, learnMoreCoveredMap: {}, learnMoreRequiredMap: {}, editHistory: {}, domainSubmissions: {}, answers: [], answerCount: '0', commentCount: '0', newCommentCount: '0', linkedMarkCount: '0', changeLogs: [ { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '11931', pageId: '425', userId: 'EricRogstad', edit: '1', type: 'newEdit', createdAt: '2016-06-07 17:56:09', auxPageId: '', oldSettingsValue: '', newSettingsValue: '' }, { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '11930', pageId: '425', userId: 'EricRogstad', edit: '1', type: 'newParent', createdAt: '2016-06-07 17:52:04', auxPageId: 'log_as_length', oldSettingsValue: '', newSettingsValue: '' } ], feedSubmissions: [], searchStrings: {}, hasChildren: 'false', hasParents: 'true', redAliases: {}, improvementTagIds: [], nonMetaTagIds: [], todos: [], slowDownMap: 'null', speedUpMap: 'null', arcPageIds: 'null', contentRequests: {} }