[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-508514-105":59,"doc-detail-508514-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","math-1510-exponential-and-logarithmic-equations-fundamentals-of-mathematics-outline","MATH 1510 - Exponential and Logarithmic Equations - Fundamentals of Mathematics - Outline","","Course outline and worked examples for solving exponential and logarithmic equations in Fundamentals of Mathematics (MATH 1510). Defines exponential equations as those with the variable in the exponent and explains solution via one-to-one properties of exponential and logarithmic functions. Includes example problems such as solving 3^(x)+2 = 7 using logarithms, and solving e^(2x) - e^x - 6 = 0 by factoring and applying domain constraints (e^x > 0).",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/math-1510-exponential-and-logarithmic-equations-fundamentals-of-mathematics-outline/508514/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/math-1510-exponential-and-logarithmic-equations-fundamentals-of-mathematics-outline/508514.png","ImageObject",300,407,{"name":92,"@type":93},"Cipher","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-05",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",15,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is an exponential equation?","Question",{"text":113,"@type":114},"An exponential equation is one in which the variable occurs in the exponent.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How are many exponential equations solved here?",{"text":118,"@type":114},"They can be solved using the one-to-one property of exponential functions (ax = ay implies x = y), allowing conversion to logarithms.",{"name":120,"@type":111,"acceptedAnswer":121},"How do logarithmic equations differ from exponential equations?",{"text":122,"@type":114},"A logarithmic equation is one in which a logarithm of the variable occurs, and it can be handled using one-to-one properties of logarithmic functions.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},508514,1791467621,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":145,"read_time":146,"preview_page_count":4},687208528416,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","MATH 1510  \nLili Shen  \nExponential and Logarithmic Equations  \nFundamentals of Mathematics  \n(MATH 1510)  \nInstructor: Lili Shen Email: [shenlili@yorku.ca](shenlili@yorku.ca)  \nDepartment of Mathematics and Statistics York University  \nJanuary 25-29, 2016  \nOutline  \nMATH 1510  \nLili Shen  \nExponential and Logarithmic Equations  \n1 Exponential and Logarithmic Equations  \nExponential equations  \nMATH 1510  \nLili Shen  \nExponential and Logarithmic Equations  \nAn exponential equation is one in which the variable occurs in the exponent.  \nSome exponential equations can be solved by using the fact that exponential functions are one-to-one, i.e. ,  \nax = ay () x = y:  \nMATH 1510  \nLili Shen  \nExponential and Logarithmic Equations  \nExponential equations  \nExample  \nSolve the exponential equation  \n3x+2 = 7 :  \nMATH 1510  \nLili Shen  \nExponential and Logarithmic Equations  \nExponential equations  \nSolution.  \n3x+2 = 7 ; log33x+2 = log3 7 ;  \nx + 2 = log3 7 ; x = log3 7 􀀀 2 :  \nExponential equations  \nMATH 1510  \nLili Shen  \nExponential and Logarithmic Equations  \nIn this example,  \nx = log3 7 􀀀 2  \nis the exact solution of the equation 3x+2 = 7.  \nUsing calculators, one could find an approximation to the exact solution by the change of base formula:  \nx = log3 7 􀀀 2 = n~~ ~~7n~~ 3~~ 􀀀 2 􀀙 􀀀 0:228756:  \nMATH 1510  \nLili Shen  \nExponential and Logarithmic Equations  \nExponential equations  \nExample  \nSolve the equation  \ne2x 􀀀 ex 􀀀 6 = 0 :  \nMATH 1510  \nLili Shen  \nExponential and Logarithmic Equations  \nExponential equations  \nSolution.  \ne2x 􀀀 ex 􀀀 6 = 0 ;( ex 􀀀 3)(ex + 2) = 0 ; ex = 3 or ex = 􀀀2:  \nSince ex > 0, one could only have ex = 3 and consequently  \nx = ln 3 :  \nLogarithmic equations  \nMATH 1510  \nLili Shen  \nExponential and Logarithmic Equations  \nA logarithmic equation is one in which a logarithm of the variable occurs.  \nSome exponential equations can be solved by using the fact that logarithmic functions are one-to-one, i.e. ,  \nloga x = loga y () x = y:  \nMATH 1510  \nLili Shen  \nExponential and Logarithmic Equations  \nLogarithmic equations  \nExample  \nSolve each equation for x.  \n(1) ln x = 8.  \n(2) log2 (25 􀀀 x) = 3.","cbCaitpVM1BXDfDE","https://ap.wps.com/l/cbCaitpVM1BXDfDE","pdf",175042,17,"English","# Exponential and Logarithmic Equations\n## Exponential equations\n## Logarithmic equations","[{\"question\":\"What is an exponential equation?\",\"answer\":\"An exponential equation is one in which the variable occurs in the exponent.\"},{\"question\":\"How are many exponential equations solved here?\",\"answer\":\"They can be solved using the one-to-one property of exponential functions (ax = ay implies x = y), allowing conversion to logarithms.\"},{\"question\":\"How do logarithmic equations differ from exponential equations?\",\"answer\":\"A logarithmic equation is one in which a logarithm of the variable occurs, and it can be handled using one-to-one properties of logarithmic functions.\"}]","MATH 1510 - Exponential and Logarithmic Equations - Fundamentals of Mathematics - Outline | PDF",1791225448,43]