[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523511-105":59,"doc-detail-523511-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","properties-of-logarithms-expand-and-condense-logarithms-worksheet","Properties of Logarithms - Expand and Condense Logarithms Worksheet","","Worksheet from Infinite Precalculus focused on the properties of logarithms. Students expand each logarithm and convert products, quotients, and powers into equivalent logarithmic expressions. A second section asks students to condense multi-log expressions into a single logarithm, applying key rules such as sum and difference of logarithms, and logarithm of a power. Critical thinking problems extend these rules using nested expressions. ",{"@graph":69,"@context":122},[70,84,105],{"@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/properties-of-logarithms-expand-and-condense-logarithms-worksheet/523511/",{"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/properties-of-logarithms-expand-and-condense-logarithms-worksheet/523511.png","ImageObject",300,407,{"name":92,"@type":93},"OmBimo","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What tasks does the worksheet ask students to do with logarithms?","Question",{"text":112,"@type":113},"It asks students to expand each logarithm and then condense expressions into a single logarithm using logarithm properties.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Where are the “critical thinking” problems located?",{"text":117,"@type":113},"At the end of the worksheet section labeled “Critical thinking questions,” following the main expand/condense exercises.",{"name":119,"@type":110,"acceptedAnswer":120},"How are answers expected to be simplified?",{"text":121,"@type":113},"For the condense section, each multi-part expression should be rewritten as one logarithm, applying the correct product/quotient/power rules.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},523511,1791710361,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":34,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":52,"preview_page_count":4},962090893581,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Kuta Software-Infinite Precalculus Name   \nProperties of Logarithms Date  Period   \nExpand each logarithm.  \n1) log 􀀕􀀖~~ ~~ 2) log (􀀖 􀂘 􀀔􀀔)  \n3) log (􀀙 􀂘 􀀚) 4) log (􀀘 􀂘 􀀔􀀔)  \n5) log (􀀚 􀂘 􀀛) 6) log ~~ ~~􀀔􀀔~~ ~~􀀕􀀔~~ ~~  \n7) log 􀀖 8) log   \n9) log (a 􀂘 b) 10) log x 􀀘  \n11) log (u 􀂘 v) 􀀙 12) log (ab 􀀘)  \nCondense each expression to a single logarithm.  \n13) log 􀀙 􀀐 log 􀀘 14) log 􀀔􀀕 􀀎 log 􀀘  \n15) log 􀀙 􀀎 log 􀀚 16) log 􀀔􀀕 􀀐 log 􀀔􀀔  \n17) 􀀖 log x 18) 􀀙 log a  \n19) log a 􀀐 log b 20) log􀀕~~ ~~x  \n21) log x 􀀎 􀀘 log y 22) 􀀙 log u 􀀐 􀀙 log v  \n23) 􀀗 log x 􀀎 􀀗 log y 24) log u 􀀎 log v 􀀎 log w  \nCritical thinking questions:  \n25) 􀀕 (log 􀀕x 􀀐 log y) 􀀐 (log 􀀖 􀀎 􀀕 log 􀀘 ) 26) log x 􀂘 log 􀀕  \nKuta Software-Infinite Precalculus Name   \nProperties of Logarithms Date  Period   \nExpand each logarithm.  \n1) log 􀀕􀀖~~ ~~ 2) loglog(􀀖􀀖􀂘  􀀔lo) g 􀀔􀀔 log 􀀕 􀀐 log 􀀖  \n3) log (􀀙 􀂘 􀀚) 4) log (􀀘 􀂘 􀀔􀀔)  \nlog 􀀙 􀀎 log 􀀚 log 􀀘 􀀎 log 􀀔􀀔  \n5) log (􀀚 􀂘 􀀛) 6) log  􀀔􀀕  log 􀀚 􀀎 log 􀀛 􀀔􀀔  \nlog 􀀔􀀕 􀀐 log 􀀔􀀔  \n7) log 􀀖 8) log   \nlog x   log x  \n􀀖 􀀕  \n9) log (a 􀂘 b) 10) log x 􀀘  \nlog a 􀀎 log b 􀀘 log x  \n11) log (u 􀂘 v) 􀀙 12) log (ab 􀀘)  \n􀀙 log u 􀀎 􀀙 log v log a 􀀎 􀀘 log b  \nCondense each expression to a single logarithm.  \n13) log 􀀙 􀀐 log 􀀘  \nlog 􀀙􀀘  \n15) log 􀀙 􀀎 log 􀀚  \nlog 􀀗􀀕  \n17) 􀀖 log x  \nlog x 􀀖  \n19) log a 􀀐 log b  \nlog ab  \n21) log x 􀀎 􀀘 log y  \nlog (xy 􀀘)  \n23) 􀀗 log x 􀀎 􀀗 log y  \nlog (y 􀀗x 􀀗)  \nCritical thinking questions:  \n25) 􀀕 (log 􀀕x 􀀐 log y) 􀀐 (log 􀀖 􀀎 􀀕 log 􀀘 )  \nlog 􀀗x􀀕􀀚􀀘~~ ~~y~~􀀕 ~~  \n14) log 􀀔􀀕 􀀎 log 􀀘  \nlog 􀀙􀀓  \n16) log 􀀔􀀕 􀀐 log 􀀔􀀔  \n 􀀔􀀕  log  \n􀀔􀀔  \n18) 􀀙 log a  \nlog a 􀀙  \n20) log􀀕~~ ~~x  \nlog   \n22) 􀀙 log u 􀀐 􀀙 log v  \nlog  \n􀀙  \nu  \n􀀙  \nv  \n24) log u 􀀎 log v 􀀎 log w  \nlog wvu  \n26) log x 􀂘 log 􀀕  \nCan't be simplified.  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaion7Prv3hL7m","https://ap.wps.com/l/cbCaion7Prv3hL7m","pdf",23942,"English","# Expand each logarithm\n## Condense each expression to a single logarithm\n# Critical thinking questions","[{\"question\":\"What tasks does the worksheet ask students to do with logarithms?\",\"answer\":\"It asks students to expand each logarithm and then condense expressions into a single logarithm using logarithm properties.\"},{\"question\":\"Where are the “critical thinking” problems located?\",\"answer\":\"At the end of the worksheet section labeled “Critical thinking questions,” following the main expand/condense exercises.\"},{\"question\":\"How are answers expected to be simplified?\",\"answer\":\"For the condense section, each multi-part expression should be rewritten as one logarithm, applying the correct product/quotient/power rules.\"}]","Properties of Logarithms - Expand and Condense Logarithms Worksheet | PDF",1791426939]