[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-289138-105":59,"doc-detail-289138-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","section-45-properties-of-logarithms-practice-exercises","Section 4.5 - Properties of Logarithms - Practice Exercises","","This document provides a set of mathematical practice exercises focused on the properties of logarithms, specifically designated for section 4.5 of a mathematics curriculum. It covers key objectives including expressing complex logarithmic expressions as sums and differences of individual logs, and condensing multiple logarithmic terms into a single expression. Students are tasked with applying logarithmic identities to handle powers, products, and quotients. These exercises are designed to reinforce foundational algebraic skills necessary for manipulating logarithmic functions, such as expanding logarithmic expressions into their simplest factored forms or simplifying them through condensation. By working through these problems, learners gain practical experience in identifying the appropriate logarithmic rules to apply in various algebraic contexts, ensuring a thorough understanding of logarithmic laws and their applications in solving equations. The content is structured to guide students step-by-step through standard transformations commonly encountered in pre-calculus and algebra courses.",{"@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/section-45-properties-of-logarithms-practice-exercises/289138/",{"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/section-45-properties-of-logarithms-practice-exercises/289138.png","ImageObject",300,407,{"name":92,"@type":93},"Mali","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-09-17",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",16,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the primary goal of the exercises in Section 4.5?","Question",{"text":113,"@type":114},"The primary goal is to practice using the properties of logarithms to expand expressions into sums and differences or condense them into a single logarithmic term.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What are the specific tasks related to powers in these logarithm problems?",{"text":118,"@type":114},"Students are instructed to express all powers as factors, utilizing the power property of logarithms to simplify the expressions.",{"name":120,"@type":111,"acceptedAnswer":121},"Are there constraints provided for the variables in the logarithmic expressions?",{"text":122,"@type":114},"Yes, constraints such as x > 1, x ≠ 0, and x > 2 are provided to ensure the logarithmic arguments remain within valid domains where the functions are defined.","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},289138,1789634619,{"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":130,"read_time":145},2336475104362,"https://ap-avatar.wpscdn.com/avatar/22000c4c46a41b752dd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786595829695023868","Section 4.5  \nProperties of Logarithms  \nOBJECTIVE 1  \nOBJECTIVE 2  \nWrite log 2 ( x 2 3x~~ ~~−1) , x>1, as a sum of logarithms . Express all powers as factors .  \nWrite log 6 ~~( ~~x~~ ~~2~~ ~~3~~ ) ~~2~~ ~~ , x ≠ 0, as a difference of logarithms . Express all powers as factors .  \nWrite ln ~~ ~~x~~(~~3x~~ ~~~~) ~~22~~ ~~ , x > 2, as a sum and difference of logarithms . Express all powers as factors .  \nOBJECTIVE 3  \nWrite each of the following as a single logarithm.  \n( a ) 3ln 2 + ln ( x 2 ) + 2  \n( b ) ~~ ~~12 loga 4 − 2 loga 5  \n( c ) − 2 loga 3 + 3loga 2 − loga ( x 2 +1)","cbCaigX3Px9Ll9UP","https://ap.wps.com/l/cbCaigX3Px9Ll9UP","pdf",731256,17,"English","# Objective 1 - Expanding Logarithmic Expressions\n# Objective 2 - Logarithmic Sums and Differences\n# Objective 3 - Condensing Logarithms into Single Terms","[{\"question\":\"What is the primary goal of the exercises in Section 4.5?\",\"answer\":\"The primary goal is to practice using the properties of logarithms to expand expressions into sums and differences or condense them into a single logarithmic term.\"},{\"question\":\"What are the specific tasks related to powers in these logarithm problems?\",\"answer\":\"Students are instructed to express all powers as factors, utilizing the power property of logarithms to simplify the expressions.\"},{\"question\":\"Are there constraints provided for the variables in the logarithmic expressions?\",\"answer\":\"Yes, constraints such as x \\u003e 1, x ≠ 0, and x \\u003e 2 are provided to ensure the logarithmic arguments remain within valid domains where the functions are defined.\"}]","Section 4.5 - Properties of Logarithms - Practice Exercises | PDF",43]