[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-522731-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-522731-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","properties-of-logarithms-infinite-algebra-2-worksheets","Properties of Logarithms - Infinite Algebra 2 Worksheets","","Infinite Algebra 2 worksheet on logarithm properties with two main tasks: expanding logarithms using product/power rules and condensing sums or differences of logarithms into a single logarithm. The sheet includes multiple practice items combining numerical coefficients, variables, and powers, plus a section of critical thinking questions that require applying the same log laws to more structured expressions. 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For critical thinking questions, carefully follow the same product/power/quotient rules and simplify only what those laws allow.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},522731,1791710359,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":33,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":123,"preview_page_count":4},687207022233,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Kuta Software-Infinite Algebra 2 Name___________________________________  \nProperties of Logarithms Date________________ Period____  \nExpand each logarithm.  \n1) log (6 ⋅ 11) 2) log (5 ⋅ 3)  \n3) log (~~ ~~611~~ ~~ ) 5 4) log (3 ⋅ 23 )  \n5) log 245~~ ~~ 6) log (~~ ~~65) 6  \n7) log ~~ ~~xy~~ ~~6~~ ~~ 8) log (a ⋅ b)2  \nu4   x   \n9) log 10) log v y 5  \n11) log 3x ⋅ y ⋅ z  12) log ( x ⋅ y ⋅ z2 )  \nCondense each expression to a single logarithm.  \n13) log 3 − log 8  log 6  \n14)  \n3  \n15) 4 log 3 − 4 log 8 16) log 2 + log 11 + log 7  \n17) log 7 − 2 log 12  2 log 7 18)  \n3  \n19) 6 log 3 u + 6 log 3 v 20) ln x − 4 ln y  \n21) log 4 u − 6 log 4 v 22) log 3 u − 5 log 3 v  \n23) 20 log 6 u + 5 log 6 v 24) 4 log 3 u − 20 log 3 v  \nCritical thinking questions:  \n25) 2(log 2x − log y) − (log 3 + 2 log 5) 26) log x ⋅ log 2  \nKuta Software-Infinite Algebra 2 Properties of Logarithms  \nExpand each logarithm.  \n1) log (6 ⋅ 11)  \nlog 6 + log 11  \n3) log (~~ ~~611) 5  \n5 log 6 − 5 log 11  \nName___________________________________  \nDate________________ Period____  \n2) log (5 ⋅ 3)  \nlog 5 + log 3  \n4) log (3 ⋅ 23 )  \nlog 3 + 3 log 2  \n5) log 245  \n4 log 2 − log 5  \n7) log  \n x   \ny 6  \nlog x − 6 log y  \n9) log u4v  \n4 log u − log v  \n6) log (~~ ~~65) 6  \n6 log 6 − 6 log 5  \n8) log (a ⋅ b)2  \n2 log a + 2 log b  \n10) log  x y 5  \nlog x − 5 log y  \n3  \n11) log  x ⋅ y ⋅ z  \nlog x log y log z ~~ ~~ + ~~ ~~ + ~~ ~~  \n3 3 3  \n12) log ( x ⋅ y ⋅ z2 )  \nlog x + log y + 2 log z  \nCondense each expression to a single logarithm.  \n13) log 3 − log 8  \nlog 38  \n15) 4 log 3 − 4 log 8  \n34 log ~~ ~~  \n84  \n17) log 7 − 2 log 12  \nlog  7   \n122  \n19) 6 log 3 u + 6 log 3 v  \nlog 3 (v6 u 6 )  \n21) log 4 u − 6 log 4 v  \n u   \nlog 4 6  \nv  \n23) 20 log 6 u + 5 log 6 v  \nlog 6 (v5 u 20 )  \nCritical thinking questions:  \n25) 2(log 2x − log y) − (log 3 + 2 log 5)  \n 4x2  log 2  \n75 y  \n14) log3~~ ~~6  \nlog 36  \n16) log 2 + log 11 + log 7  \nlog 154  \n18) 2~~ ~~lo3g~~ ~~7  \nlog 7  \n3  \n2  \n20) ln x − 4 ln y  \nln  x y4  \n22) log 3 u − 5 log 3 v  \n u  log 3 5  \nv  \n24) 4 log 3 u − 20 log 3 v  \n u 4   \nlog 3  \nv 20  \n26) log x ⋅ log 2  \nCan't be simplified.  \nCreate your own worksheets like this one with Infinite Algebra 2. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaisxpkKi26OcS","https://ap.wps.com/l/cbCaisxpkKi26OcS","pdf",34385,"English","# Expand each logarithm\n## Condense each expression to a single logarithm\n## Critical thinking questions","[{\"question\":\"How do I expand a logarithm of a product or power on this worksheet?\",\"answer\":\"Use the logarithm product rule to split log(a·b) into log a + log b, and use the power rule to move exponents: log(a^k) = k·log a.\"},{\"question\":\"How do I condense multiple logarithms into one?\",\"answer\":\"Combine terms by applying inverses of the expansion rules: add logs as a product, and multiply coefficients as exponents, so expressions like m·log a + n·log b become log(a^m·b^n).\"},{\"question\":\"What should I do for the “can’t be simplified” or critical thinking items?\",\"answer\":\"If the worksheet indicates it can’t be simplified, stop and keep the given structure. For critical thinking questions, carefully follow the same product/power/quotient rules and simplify only what those laws allow.\"}]","Properties of Logarithms - Infinite Algebra 2 Worksheets | PDF",1791426106]