{"id":6738,"date":"2014-01-30T17:28:26","date_gmt":"2014-01-30T17:28:26","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6738"},"modified":"2014-12-02T08:25:33","modified_gmt":"2014-12-02T08:25:33","slug":"math-review-of-logarithms","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-logarithms\/","title":{"rendered":"Math Review of Logarithms"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

Logarithms are useful shorthand to express exponential values.\u00a0 They have many common applications in mathematics, science, and engineering.<\/p>\n

What Is the Relationship Between Logarithms and Exponents?<\/strong><\/p>\n

The number 10,000 is equal in exponential form to 104<\/sup>, where 10 is the base and 4 is the exponent.\u00a0 In logarithmic form, log10<\/sub> 10,000 is equal to 4.\u00a0\u00a0Similarly, log10<\/sub>100,000 is equal to 5.\u00a0 Many \u00a0bases \u00a0can be used in deriving logarithms, as the base can be any positive number that is greater than 1.\u00a0 For example log2<\/sub> 4 is equal to 2, because 22<\/sup> equals 4, and log2 <\/sub>8 is equal to 3.<\/p>\n

What Are Some Properties of Logarithms?<\/strong><\/p>\n

One of the most useful properties of logarithms is that logarithms can be multiplied by adding them.\u00a0 This makes calculations much less complex.\u00a0 For example, \u00a0log2<\/sub> 32 is equal to 5 and log2<\/sub> 128 is equal to 7.\u00a0 What is log2 <\/sub>of 4096?\u00a0 The number 4096 is equal to 32\u2219128.\u00a0 Another way to express this relationship is that log2 <\/sub>32 + log2<\/sub>128 is equal to log2 <\/sub>4096.\u00a0 This is correct because log2<\/sub> 4096 is equal to 12, and so is 5 + 7.\u00a0 Similarly, logarithms can be divided by subtracting them,\u00a0 For example,\u00a0 log10 <\/sub>of 1000 is 3 and log10 <\/sub>of 100 is 2.\u00a0 The number 1000 divided by 100 is 10, and 103<\/sup>\/102<\/sup> is also 10 or 101<\/sup>.\u00a0 By definition, log10 <\/sub>10 is equal to 1 or 3-2.<\/p>\n

What Are the Natural and Common Logarithms?<\/strong><\/p>\n

The natural logarithm has a base that is an irrational number roughly equal to 2.71828.\u00a0 It is useful in many mathematical relationships, such as growth rate.\u00a0 It is represented on many calculators by the abbreviation ln, The common logarithm is the base10<\/sub> logarithm.\u00a0 It is often represented as log without a subscript.\u00a0 The numerical system that we use for counting is base 10.<\/p>\n

How Are Logarithms Used?<\/strong><\/p>\n

Logarithms are often used in applied calculations in many branches of science.\u00a0 The Richter scale, used to measure the strength of earthquakes, is a logarithmic scale.\u00a0 An earthquake of magnitude 4 is 10 times stronger than an earthquake of magnitude 3 and 1000 times stronger than magnitude 1.\u00a0 The pH value of a liquid in chemistry is also measured on a logarithmic scale.<\/p>\n

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Overview: Logarithms are useful shorthand to express exponential values.\u00a0 They have many common applications in mathematics, science, and engineering. What Is the Relationship Between Logarithms and Exponents? The number 10,000 is equal in exponential form to 104, where 10 is the base and 4 is the exponent.\u00a0 In logarithmic form, log10 10,000 is equal to […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[2613,1060,2612],"class_list":["post-6738","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-common-logarithm","tag-logarithm","tag-natural-logarithm"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6738","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=6738"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6738\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6738"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6738"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6738"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}