{"id":8876,"date":"2020-12-08T12:05:51","date_gmt":"2020-12-08T06:35:51","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=8876"},"modified":"2020-12-08T14:56:49","modified_gmt":"2020-12-08T09:26:49","slug":"logarithmic-expressions","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/logarithmic-expressions\/","title":{"rendered":"Logarithmic Expressions"},"content":{"rendered":"<h2><span style=\"color: #3366ff;\"><strong>Logarithmic Expressions<\/strong><\/span><\/h2>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-127699\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-1.jpg\" alt=\"Logarithmic Expressions 1\" width=\"638\" height=\"479\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-1.jpg 638w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-1-300x225.jpg 300w\" sizes=\"(max-width: 638px) 100vw, 638px\" \/><\/p>\n<p>A logarithm is an exponent.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-127700\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-2.jpg\" alt=\"Logarithmic Expressions 2\" width=\"226\" height=\"113\" \/><br \/>\nIn the example shown above, 3 is the exponent to which the base 2 must be raised to create the answer of 8, or \\(2^3\\) =\u00a0= 8. In this example, 8 is called the anitlogarithm base 2 of 3.<\/p>\n<p><strong>Read also:<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/cbselibrary.com\/logarithms-work\/\">How do Logarithms Work?<\/a><\/li>\n<li><a href=\"https:\/\/cbselibrary.com\/logarithmic-equations\/\">Logarithmic Equations<\/a><\/li>\n<li><a href=\"https:\/\/cbselibrary.com\/logarithmic-functions\/\">Logarithmic Functions<\/a><\/li>\n<li><a href=\"https:\/\/cbselibrary.com\/logarithmic-series-expansion\/\">What is Logarithmic Series Expansion?<\/a><\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-127701\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-3.jpg\" alt=\"Logarithmic Expressions 3\" width=\"638\" height=\"479\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-3.jpg 638w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-3-300x225.jpg 300w\" sizes=\"(max-width: 638px) 100vw, 638px\" \/><\/p>\n<p>Try to remember the &#8220;spiral&#8221; relationship between the values as shown at the right. Follow the arrows starting with base 2 to get the equivalent exponential form.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-127703\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-4.jpg\" alt=\"Logarithmic Expressions 4\" width=\"181\" height=\"124\" \/><br \/>\nLogarithms with base 10 are called common logarithms.<br \/>\nWhen the base is not indicated, base 10 is implied.<\/p>\n<p>Logarithms with base e are called natural logarithms.<br \/>\nNatural logarithms are denoted by ln.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-127704\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-5.png\" alt=\"Logarithmic Expressions 5\" width=\"660\" height=\"386\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-5.png 660w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-5-300x175.png 300w\" sizes=\"(max-width: 660px) 100vw, 660px\" \/><\/p>\n<p>On the graphing calculator:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-127705\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-6.jpg\" alt=\"Logarithmic Expressions 6\" width=\"251\" height=\"316\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-6.jpg 251w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-6-238x300.jpg 238w\" sizes=\"(max-width: 251px) 100vw, 251px\" \/><\/p>\n<p>The base 10 logarithm is the log key.<br \/>\nThe base e logarithm is the ln key.<br \/>\nTo enter a logarithm with a different base,<br \/>\nuse the Change of Base Formula:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-127706\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-7.jpg\" alt=\"Logarithmic Expressions 7\" width=\"136\" height=\"66\" \/><\/p>\n<p><iframe loading=\"lazy\" title=\"Condensing Logarithms\" width=\"1200\" height=\"900\" src=\"https:\/\/www.youtube.com\/embed\/GiBcrISbTuM?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/p>\n<p><strong>Properties of Logs:<\/strong><br \/>\nUsing the properties of exponents, we can arrive at the properties of logarithms.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-127707\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-8.jpg\" alt=\"Logarithmic Expressions 8\" width=\"738\" height=\"489\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-8.jpg 738w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-8-300x199.jpg 300w\" sizes=\"(max-width: 738px) 100vw, 738px\" \/><\/p>\n<p>Examples:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-127709\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-9.jpg\" alt=\"Logarithmic Expressions 9\" width=\"654\" height=\"970\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-9.jpg 654w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Logarithmic-Expressions-9-202x300.jpg 202w\" sizes=\"(max-width: 654px) 100vw, 654px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Logarithmic Expressions A logarithm is an exponent. In the example shown above, 3 is the exponent to which the base 2 must be raised to create the answer of 8, or =\u00a0= 8. In this example, 8 is called the anitlogarithm base 2 of 3. Read also: How do Logarithms Work? Logarithmic Equations Logarithmic Functions &#8230; <a title=\"Logarithmic Expressions\" class=\"read-more\" href=\"https:\/\/cbselibrary.com\/logarithmic-expressions\/\" aria-label=\"More on Logarithmic Expressions\">Read more<\/a><\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[3239],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v18.4.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Logarithmic Expressions - CBSE Library<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/cbselibrary.com\/logarithmic-expressions\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Logarithmic Expressions\" \/>\n<meta property=\"og:description\" content=\"Logarithmic Expressions A logarithm is an exponent. 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