[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-434871-105":59,"doc-detail-434871-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","212-logarithmic-function-manipulation-ap-precalculus-practice","2.12 Logarithmic Function Manipulation - AP Precalculus - Practice","","Practice set for AP Precalculus Unit 2.12 on logarithmic function manipulation. Exercises focus on rewriting logarithmic expressions as sums, differences, or single logs, applying exponent and root rules, and using properties to combine or simplify terms. Additional tasks include change-of-base calculations to express logs with base 10 or base e, approximating logarithm values to the nearest thousandth, and analyzing transformed functions by determining domain and range. The sheet also includes multiple-choice equivalence and non-equivalence questions.",{"@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/212-logarithmic-function-manipulation-ap-precalculus-practice/434871/",{"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/212-logarithmic-function-manipulation-ap-precalculus-practice/434871.png","ImageObject",300,407,{"name":92,"@type":93},"acoobca","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-20","2026-09-29",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you rewrite a logarithmic expression as a sum or difference of logs?","Question",{"text":112,"@type":113},"Use logarithm rules to separate products into sums, quotients into differences, and powers into coefficients. Then rewrite the expression using the corresponding log identities.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What does “change of base” mean for logarithms in this practice?",{"text":117,"@type":113},"Convert each logarithm to base 10 or base e using change-of-base formulas, and then compute the value with a calculator.",{"name":119,"@type":110,"acceptedAnswer":120},"How do transformations affect the domain and range of the logarithmic function?",{"text":121,"@type":113},"Describe the transformation (shifts, reflections, scaling) and apply it to the base function’s restrictions, then state the resulting domain and range for the transformed graph.","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},434871,1791164361,{"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":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"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":39},3985747870733,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","2.12 Logarithmic Function Manipulation  \nAP Precalculus  \n2.12 Practice  \n\n| Instructions: Let x and y be positive constants. Write each expression as a sum or difference of logarithms. |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- |\n| 1. 􀀡􀀢􀀣 ! (􀀥􀀦 ! )\u003Cbr>|  | \"!\u003Cbr>2. ln ~~ ~~\\# \"\u003Cbr>| | | |  |\n|  |  | |  |  |  |  |\n|  |  |  |  |  |  |  |\n| 3. log 1000􀀥!\u003Cbr>\u003Cbr>|  | 4. 􀀡􀀢􀀣$ (8√􀀥) \u003Cbr>\u003Cbr>\u003Cbr>|  |  |  |  |\n| 5. 􀀡􀀢􀀣$ 0%&\\#\"!\"\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>|  | 6. 􀀡􀀢􀀣 ! (9􀀥 − 27)\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>|  |  |  |  |\n| Instructions: Let x and y be positive constants. Write each as a single logarithm. |  |  |  |  |  |  |\n| 7. ln 3 + ln 􀀥\u003Cbr>| 8. 2􀀡􀀢􀀣!􀀥 − 4􀀡􀀢􀀣!􀀦\u003Cbr>|  |  |  |  |  |\n| 9. %$ (log 􀀥 + 3 log 􀀦)\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>| 10. 3􀀡􀀢􀀣 (􀀥 − 4) − 2􀀡􀀢􀀣 􀀦\u003Cbr>' '\u003Cbr>|  |  |  |  |  |\n\n© The Algebros [from FlippedMath.com](from FlippedMath.com)  \n\n| CALCULATOR ACTIVE: Instructions: Use the change of base to change each to a logarithm with base 10 or base e. Then use a calculator and find the value of the logarithm to the nearest thousandth. |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- |\n| 11. 􀀡􀀢􀀣( 123\u003Cbr>| | | 12. 􀀡􀀢􀀣 )578\u003Cbr>\u003Cbr>| | |\n| Instructions: Describe any transformations on the function, then find the domain and range of the transformed function. |  |  |  |  |  |\n| 13. 􀀹(􀀥) = 􀀡􀀢􀀣( 16􀀥\u003Cbr>|  |  | 14. 􀀣 (􀀥) = 􀀡􀀢􀀣$ \u003C\"*\u003Cbr>=\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>|  |  |\n\n2.12 Logarithmic Function Manipulation  2.12 Test Prep    \n17. Let x and y be positive constants. Which of the following is equivalent to 5 log 􀀥 + 6 log 􀀦 .  \n(A) log(􀀥! + 􀀧\" )  \n (B) log(􀀥!􀀧 \" )   \n(C) log(􀀥! − 􀀧\" )  \n(D) log(5􀀥 + 6􀀧)  \n© The Algebros [from FlippedMath.com](from FlippedMath.com)  \n18. Let x and y be positive constants. Which of the following is NOT equivalent to:  \n􀀡􀀢􀀣 ! (􀀥 + 3) + 2􀀡􀀢􀀣! (􀀥 − 1) − 􀀡􀀢􀀣! (􀀥 + 2) .  \n19. If log 3 = 􀀥 and log 4 = 􀀦 , which of the following expresses log √12 ?  \n20. Approximate 􀀡􀀢􀀣-18, given that 􀀡􀀢􀀣-2 ≈ .4307 and 􀀡􀀢􀀣-3 ≈ .6827.  \n(A) 0.8968  \n(B) 1.1134  \n(C) 1.5441  \n(D) 1.7961  \n© The Algebros [from FlippedMath.com](from FlippedMath.com)","cbCaivQpxfcW3h1F","https://ap.wps.com/l/cbCaivQpxfcW3h1F","pdf",1336914,"English","# 2.12 Logarithmic Function Manipulation - AP Precalculus - Practice\n## Write as sums or differences of logarithms\n## Write as a single logarithm\n## Change of base and evaluate with a calculator\n## Transformations, domain, and range\n## Multiple-choice equivalence and approximation questions","[{\"question\":\"How do you rewrite a logarithmic expression as a sum or difference of logs?\",\"answer\":\"Use logarithm rules to separate products into sums, quotients into differences, and powers into coefficients. Then rewrite the expression using the corresponding log identities.\"},{\"question\":\"What does “change of base” mean for logarithms in this practice?\",\"answer\":\"Convert each logarithm to base 10 or base e using change-of-base formulas, and then compute the value with a calculator.\"},{\"question\":\"How do transformations affect the domain and range of the logarithmic function?\",\"answer\":\"Describe the transformation (shifts, reflections, scaling) and apply it to the base function’s restrictions, then state the resulting domain and range for the transformed graph.\"}]","2.12 Logarithmic Function Manipulation - AP Precalculus - Practice | PDF",1790670914]