{"id":1476,"date":"2020-03-27T13:46:31","date_gmt":"2020-03-27T13:46:31","guid":{"rendered":"http:\/\/ibalmaths.com\/?post_type=knowledgebase&#038;p=1476"},"modified":"2020-03-27T15:26:57","modified_gmt":"2020-03-27T15:26:57","slug":"ibdp-past-year-exam-questions-exponents-and-logarithms","status":"publish","type":"knowledgebase","link":"https:\/\/ibalmaths.com\/index.php\/ibdp-math-hl-2\/exponents-and-logarithms\/ibdp-past-year-exam-questions-exponents-and-logarithms\/","title":{"rendered":"IBDP Past Year Exam Questions &#8211; Exponents and Logarithms"},"content":{"rendered":"<p><strong>1.\u00a0 \u00a0[M12\/P1\/TZ1]<\/strong><\/p>\r\n<p>Solve the equation\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2<\/mn><mo>&#160;<\/mo><mo>&#8211;<\/mo><mo>&#160;<\/mo><msub><mi>log<\/mi><mn>3<\/mn><\/msub><mo>(<\/mo><mi>x<\/mi><mo>+<\/mo><mn>7<\/mn><mo>)<\/mo><mo>=<\/mo><msub><mi>log<\/mi><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><\/msub><mn>2<\/mn><mi>x<\/mi><\/math>\r\n .\u00a0 \u00a0[5 marks]<\/p>\r\n<div id=\"link1-link-1476\" class=\"sh-link link1-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link1', 1476, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link1-toggle-1476\">Solution<\/span><\/a><\/div><div id=\"link1-content-1476\" class=\"sh-content link1-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1479\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/1-17.jpg\" alt=\"\" width=\"971\" height=\"274\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/1-17.jpg 971w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/1-17-300x85.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/1-17-768x217.jpg 768w\" sizes=\"auto, (max-width: 971px) 100vw, 971px\" \/><\/p>\r\n<p><\/div>\r\n<p><strong>2.\u00a0 \u00a0[M13\/P1\/TZ1]<\/strong><\/p>\r\n<p>The first terms of an arithmetic sequence are\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>1<\/mn><mrow><msub><mi>log<\/mi><mn>2<\/mn><\/msub><mi>x<\/mi><\/mrow><\/mfrac><mo>,<\/mo><mo>&#160;<\/mo><mfrac><mn>1<\/mn><mrow><msub><mi>log<\/mi><mn>8<\/mn><\/msub><mi>x<\/mi><\/mrow><\/mfrac><mo>,<\/mo><mo>&#160;<\/mo><mfrac><mn>1<\/mn><mrow><msub><mi>log<\/mi><mn>32<\/mn><\/msub><mi>x<\/mi><\/mrow><\/mfrac><mo>,<\/mo><mo>&#160;<\/mo><mfrac><mn>1<\/mn><mrow><msub><mi>log<\/mi><mn>128<\/mn><\/msub><mi>x<\/mi><\/mrow><\/mfrac><mo>,<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><\/math>\r\n<\/p>\r\n<p>Find x if the sum of the first 20 terms of the sequence is equal to 100.\u00a0 \u00a0[6 marks]<\/p>\r\n<div id=\"link2-link-1476\" class=\"sh-link link2-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link2', 1476, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link2-toggle-1476\">Solution<\/span><\/a><\/div><div id=\"link2-content-1476\" class=\"sh-content link2-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1481\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/2-11.jpg\" alt=\"\" width=\"971\" height=\"1183\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/2-11.jpg 971w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/2-11-246x300.jpg 246w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/2-11-840x1024.jpg 840w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/2-11-768x936.jpg 768w\" sizes=\"auto, (max-width: 971px) 100vw, 971px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>3.\u00a0 \u00a0[M14\/P1\/TZ1]<\/strong><\/p>\r\n<p>Consider \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mo>=<\/mo><msub><mi>log<\/mi><mn>2<\/mn><\/msub><mn>3<\/mn><mo>&#215;<\/mo><msub><mi>log<\/mi><mn>3<\/mn><\/msub><mn>4<\/mn><mo>&#215;<\/mo><msub><mi>log<\/mi><mn>4<\/mn><\/msub><mn>5<\/mn><mo>&#215;<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>&#215;<\/mo><msub><mi>log<\/mi><mn>31<\/mn><\/msub><mn>32<\/mn><\/math>\r\n . Given that\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mo>&#8712;<\/mo><mi mathvariant=\"normal\">&#8484;<\/mi><\/math>\r\n , find the value of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><\/math>\r\n .\u00a0 \u00a0[5 marks]<\/p>\r\n<div id=\"link3-link-1476\" class=\"sh-link link3-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link3', 1476, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link3-toggle-1476\">Solution<\/span><\/a><\/div><div id=\"link3-content-1476\" class=\"sh-content link3-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1483\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/3-9.jpg\" alt=\"\" width=\"994\" height=\"311\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/3-9.jpg 994w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/3-9-300x94.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/3-9-768x240.jpg 768w\" sizes=\"auto, (max-width: 994px) 100vw, 994px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>4.\u00a0 \u00a0[M14\/P1\/TZ2]<\/strong><\/p>\r\n<p>Solve the equation\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>8<\/mn><mrow><mi>x<\/mi><mo>&#8211;<\/mo><mn>1<\/mn><\/mrow><\/msup><mo>=<\/mo><msup><mn>6<\/mn><mrow><mn>3<\/mn><mi>x<\/mi><\/mrow><\/msup><\/math>\r\n . Express your answer in terms of ln2 and ln3 .\u00a0 \u00a0[5 marks]<\/p>\r\n<div id=\"link4-link-1476\" class=\"sh-link link4-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link4', 1476, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link4-toggle-1476\">Solution<\/span><\/a><\/div><div id=\"link4-content-1476\" class=\"sh-content link4-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1485\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/4-10.jpg\" alt=\"\" width=\"1000\" height=\"1123\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/4-10.jpg 1000w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/4-10-267x300.jpg 267w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/4-10-912x1024.jpg 912w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/4-10-768x862.jpg 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>5.\u00a0 \u00a0[N13\/P1\/TZ0]<\/strong><\/p>\r\n<p>Solve the following equations:<\/p>\r\n<p>(a)\u00a0 \u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>log<\/mi><mn>2<\/mn><\/msub><mfenced><mrow><mi>x<\/mi><mo>&#8211;<\/mo><mn>2<\/mn><\/mrow><\/mfenced><mo>=<\/mo><msub><mi>log<\/mi><mn>4<\/mn><\/msub><mfenced><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>&#160;<\/mo><mo>&#8211;<\/mo><mo>&#160;<\/mo><mn>6<\/mn><mi>x<\/mi><mo>&#160;<\/mo><mo>+<\/mo><mn>12<\/mn><\/mrow><\/mfenced><\/math>\r\n ;\u00a0 \u00a0[3 marks]<\/p>\r\n<p>(b)\u00a0 \u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>x<\/mi><mrow><mi>ln<\/mi><mi>x<\/mi><\/mrow><\/msup><mo>=<\/mo><msup><mi>e<\/mi><msup><mfenced><mrow><mi>ln<\/mi><mo>&#160;<\/mo><mi>x<\/mi><\/mrow><\/mfenced><mn>3<\/mn><\/msup><\/msup><\/math>\r\n .\u00a0 [5 marks]<\/p>\r\n<div id=\"link5-link-1476\" class=\"sh-link link5-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link5', 1476, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link5-toggle-1476\">Solution<\/span><\/a><\/div><div id=\"link5-content-1476\" class=\"sh-content link5-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1488\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/5-8.jpg\" alt=\"\" width=\"996\" height=\"942\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/5-8.jpg 996w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/5-8-300x284.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/5-8-768x726.jpg 768w\" sizes=\"auto, (max-width: 996px) 100vw, 996px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>6.\u00a0 \u00a0[M09\/P1\/TZ1]<\/strong><\/p>\r\n<p>Let\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>g<\/mi><mfenced><mi>x<\/mi><\/mfenced><mo>=<\/mo><msub><mi>log<\/mi><mn>5<\/mn><\/msub><mfenced open=\"|\" close=\"|\"><mrow><mn>2<\/mn><msub><mi>log<\/mi><mn>3<\/mn><\/msub><mo>&#160;<\/mo><mi>x<\/mi><\/mrow><\/mfenced><\/math>\r\n . Find the product of the zeros of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>g<\/mi><\/math>\r\n .\u00a0 \u00a0[5 marks]<\/p>\r\n<div id=\"link6-link-1476\" class=\"sh-link link6-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link6', 1476, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link6-toggle-1476\">Solution<\/span><\/a><\/div><div id=\"link6-content-1476\" class=\"sh-content link6-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1490\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/6-11.jpg\" alt=\"\" width=\"935\" height=\"313\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/6-11.jpg 935w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/6-11-300x100.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/03\/6-11-768x257.jpg 768w\" sizes=\"auto, (max-width: 935px) 100vw, 935px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p>&nbsp;<\/p><!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"1.\u00a0 \u00a0[M12\/P1\/TZ1] Solve the equation\u00a0 2&#160;&#8211;&#160;log3(x+7)=log132x .\u00a0 \u00a0[5 marks] 2.\u00a0 \u00a0[M13\/P1\/TZ1] The first terms of an arithmetic sequence are\u00a0 1log2x,&#160;1log8x,&#160;1log32x,&#160;1log128x,&#8230;.. Find x if the sum of the first 20 terms of the sequence is equal to 100.\u00a0 \u00a0[6 marks] 3.\u00a0 \u00a0[M14\/P1\/TZ1] Consider a=log23&#215;log34&#215;log45&#215;&#8230;&#215;log3132 . Given that\u00a0 a&#8712;&#8484; , find the value of\u00a0 a .\u00a0 \u00a0[5 [&hellip;]<!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt -->","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1476","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-exponents-and-logarithms","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1476","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1476"}],"version-history":[{"count":10,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1476\/revisions"}],"predecessor-version":[{"id":1492,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1476\/revisions\/1492"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1476"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}