{"id":548,"date":"2020-01-26T14:22:02","date_gmt":"2020-01-26T14:22:02","guid":{"rendered":"http:\/\/localhost\/?post_type=knowledgebase&#038;p=548"},"modified":"2020-10-19T04:24:09","modified_gmt":"2020-10-19T04:24:09","slug":"ibdp-math-hl-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-math-hl-past-year-exam-questions-exponents-and-logarithms\/","title":{"rendered":"Exponents and Logarithms &#8211; Practice questions"},"content":{"rendered":"<p>Q1. If\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>3<\/mn><mi>x<\/mi><\/msup><mo>=<\/mo><msup><mn>5<\/mn><mrow><mi>x<\/mi><mo>&#8211;<\/mo><mn>1<\/mn><\/mrow><\/msup><mspace linebreak=\"newline\"><\/mspace><\/math>\r\n \u00a0, find the value of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><\/math>\r\n \u00a0if\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math>\r\n \u00a0can be written as \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>log<\/mi><mi>a<\/mi><\/msub><mfenced><mfrac><mn>1<\/mn><mn>5<\/mn><\/mfrac><\/mfenced><\/math>\r\n .<\/p>\r\n<div id=\"link1-link-548\" class=\"sh-link link1-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link1', 548, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link1-toggle-548\">Solution<\/span><\/a><\/div><div id=\"link1-content-548\" class=\"sh-content link1-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p>Coming soon<br \/>\r\n<\/div>\r\n<p>Q2.\u00a0Solve for\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math>\r\n \u00a0: \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>e<\/mi><mrow><mn>2<\/mn><mi>ln<\/mi><mfenced><mrow><mi>ln<\/mi><mi>x<\/mi><\/mrow><\/mfenced><\/mrow><\/msup><mo>=<\/mo><mn>2<\/mn><mo>&#8211;<\/mo><mn>3<\/mn><mi>ln<\/mi><mi>x<\/mi><mo>&#8211;<\/mo><msup><mfenced><mrow><mi>ln<\/mi><mi>x<\/mi><\/mrow><\/mfenced><mn>2<\/mn><\/msup><\/math>\r\n .<\/p>\r\n<div id=\"link2-link-548\" class=\"sh-link link2-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link2', 548, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link2-toggle-548\">Solution<\/span><\/a><\/div><div id=\"link2-content-548\" class=\"sh-content link2-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p>Coming soon<br \/>\r\n<\/div>\r\n<p>Q3.\u00a0Solve for\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math>\r\n \u00a0:\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>log<\/mi><mfenced><mrow><mi>x<\/mi><mo>&#8211;<\/mo><mn>2<\/mn><\/mrow><\/mfenced><\/msub><mfenced><mrow><mi>x<\/mi><mo>&#8211;<\/mo><mn>1<\/mn><\/mrow><\/mfenced><mo>+<\/mo><mn>1<\/mn><mo>&#62;<\/mo><msub><mi>log<\/mi><mfenced><mrow><mi>x<\/mi><mo>&#8211;<\/mo><mn>2<\/mn><\/mrow><\/mfenced><\/msub><mn>6<\/mn><\/math>\r\n .<\/p>\r\n<div id=\"link3-link-548\" class=\"sh-link link3-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link3', 548, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link3-toggle-548\">Solution<\/span><\/a><\/div><div id=\"link3-content-548\" class=\"sh-content link3-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p>Coming soon<br \/>\r\n<\/div>\r\n<p>Q4.\u00a0Solve for\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math>\r\n \u00a0:\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>log<\/mi><mn>2<\/mn><\/msub><mi>x<\/mi><mo>&#160;<\/mo><msub><mi>log<\/mi><mn>3<\/mn><\/msub><mi>x<\/mi><mo>&#160;<\/mo><msub><mi>log<\/mi><mn>4<\/mn><\/msub><mi>x<\/mi><mo>=<\/mo><msub><mi>log<\/mi><mn>2<\/mn><\/msub><mi>x<\/mi><mo>&#160;<\/mo><mo>&#160;<\/mo><msub><mi>log<\/mi><mn>3<\/mn><\/msub><mi>x<\/mi><mo>+<\/mo><msub><mi>log<\/mi><mn>3<\/mn><\/msub><mi>x<\/mi><mo>&#160;<\/mo><msub><mi>log<\/mi><mn>4<\/mn><\/msub><mi>x<\/mi><mo>+<\/mo><msub><mi>log<\/mi><mn>4<\/mn><\/msub><mi>x<\/mi><mo>&#160;<\/mo><msub><mi>log<\/mi><mn>2<\/mn><\/msub><mi>x<\/mi><\/math>\r\n .<\/p>\r\n<div id=\"link4-link-548\" class=\"sh-link link4-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link4', 548, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link4-toggle-548\">Solution<\/span><\/a><\/div><div id=\"link4-content-548\" class=\"sh-content link4-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p>Coming soon<br \/>\r\n<\/div>\r\n<p>Q5.\u00a0If\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>log<\/mi><mn>70<\/mn><\/msub><mn>5<\/mn><mo>=<\/mo><mi>a<\/mi><\/math>\r\n \u00a0,\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>log<\/mi><mn>70<\/mn><\/msub><mn>7<\/mn><mo>=<\/mo><mi>b<\/mi><\/math>\r\n find the value of\u00a0 \u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>log<\/mi><mn>70<\/mn><\/msub><mfenced><mfrac><mn>1<\/mn><mn>8<\/mn><\/mfrac><\/mfenced><\/math>\r\n in terms of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><\/math>\r\n \u00a0 and\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>b<\/mi><\/math>\r\n \u00a0.<\/p>\r\n<div id=\"link5-link-548\" class=\"sh-link link5-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link5', 548, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link5-toggle-548\">Solution<\/span><\/a><\/div><div id=\"link5-content-548\" class=\"sh-content link5-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p>Coming soon<br \/>\r\n<\/div>\r\n<p>Q6.\u00a0Solve for\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math>\r\n \u00a0:\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>log<\/mi><mn>9<\/mn><\/msub><mi>x<\/mi><mo>=<\/mo><msub><mi>log<\/mi><mn>3<\/mn><\/msub><mfenced><mrow><mi>x<\/mi><mo>&#8211;<\/mo><mn>2<\/mn><\/mrow><\/mfenced><\/math>\r\n \u00a0.<\/p>\r\n<div id=\"link6-link-548\" class=\"sh-link link6-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link6', 548, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link6-toggle-548\">Solution<\/span><\/a><\/div><div id=\"link6-content-548\" class=\"sh-content link6-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p>Coming soon<br \/>\r\n<\/div>\r\n<p>Q7.\u00a0Find the value of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math>\r\n \u00a0for which\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>x<\/mi><mrow><msub><mi>log<\/mi><mn>3<\/mn><\/msub><mi>x<\/mi><\/mrow><\/msup><mo>&#62;<\/mo><mn>3<\/mn><\/math>\r\n \u00a0.<\/p>\r\n<div id=\"link7-link-548\" class=\"sh-link link7-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link7', 548, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link7-toggle-548\">Solution<\/span><\/a><\/div><div id=\"link7-content-548\" class=\"sh-content link7-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p>Coming soon<br \/>\r\n<\/div>\r\n<p>Q8.\u00a0Find the solution of the equation\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>3<\/mn><mi>x<\/mi><\/msup><mo>=<\/mo><msup><mi>x<\/mi><mn>3<\/mn><\/msup><\/math>\r\n \u00a0.<\/p>\r\n<div id=\"link8-link-548\" class=\"sh-link link8-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link8', 548, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link8-toggle-548\">Solution<\/span><\/a><\/div><div id=\"link8-content-548\" class=\"sh-content link8-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p>Coming soon<br \/>\r\n<\/div>\r\n<p>Q9.\u00a0Solve for\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math>\r\n \u00a0: \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>log<\/mi><mfenced><mrow><mi>x<\/mi><mo>+<\/mo><mn>5<\/mn><\/mrow><\/mfenced><mo>=<\/mo><mi>log<\/mi><mfenced><mrow><mi>x<\/mi><mo>&#8211;<\/mo><mn>1<\/mn><\/mrow><\/mfenced><\/math>\r\n .<\/p>\r\n<div id=\"link9-link-548\" class=\"sh-link link9-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link9', 548, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link9-toggle-548\">Solution<\/span><\/a><\/div><div id=\"link9-content-548\" class=\"sh-content link9-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p>Coming soon<br \/>\r\n<\/div>\r\n<p>Q10.\u00a0Find the value of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math>\r\n if: \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>log<\/mi><mn>3<\/mn><\/msub><mfenced><mrow><mn>10<\/mn><mo>&#8211;<\/mo><msup><mn>3<\/mn><mi>x<\/mi><\/msup><\/mrow><\/mfenced><mo>=<\/mo><mn>2<\/mn><mo>&#8211;<\/mo><mi>x<\/mi><\/math>\r\n .<\/p>\r\n<div id=\"link10-link-548\" class=\"sh-link link10-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link10', 548, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link10-toggle-548\">Solution<\/span><\/a><\/div><div id=\"link10-content-548\" class=\"sh-content link10-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p>Coming soon<br \/>\r\n<\/div>\r\n<p>Q11.\u00a0If\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>log<\/mi><mn>9<\/mn><\/msub><mfenced><mrow><mo>&#160;<\/mo><msub><mi>log<\/mi><mn>3<\/mn><\/msub><mi>x<\/mi><\/mrow><\/mfenced><mo>+<\/mo><msub><mi>log<\/mi><mn>3<\/mn><\/msub><mfenced><mrow><msub><mi>log<\/mi><mn>27<\/mn><\/msub><mi>x<\/mi><\/mrow><\/mfenced><mo>=<\/mo><mn>2<\/mn><\/math>\r\n , then find the value of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math>\r\n \u00a0in the form of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>a<\/mi><mi>b<\/mi><\/msup><\/math>\r\n , where\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mo>,<\/mo><mo>&#160;<\/mo><mi>b<\/mi><mo>&#8712;<\/mo><msup><mi mathvariant=\"normal\">&#8484;<\/mi><mo>+<\/mo><\/msup><\/math>\r\n .<\/p>\r\n<div id=\"link11-link-548\" class=\"sh-link link11-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link11', 548, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link11-toggle-548\">Solution<\/span><\/a><\/div><div id=\"link11-content-548\" class=\"sh-content link11-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p>Coming soon<br \/>\r\n<\/div><!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"Q1. If\u00a0 3x=5x&#8211;1 \u00a0, find the value of\u00a0 a \u00a0if\u00a0 x \u00a0can be written as loga15 . Q2.\u00a0Solve for\u00a0 x \u00a0: e2lnlnx=2&#8211;3lnx&#8211;lnx2 . Q3.\u00a0Solve for\u00a0 x \u00a0:\u00a0 logx&#8211;2x&#8211;1+1&#62;logx&#8211;26 . Q4.\u00a0Solve for\u00a0 x \u00a0:\u00a0 log2x&#160;log3x&#160;log4x=log2x&#160;&#160;log3x+log3x&#160;log4x+log4x&#160;log2x . Q5.\u00a0If\u00a0 log705=a \u00a0,\u00a0 log707=b find the value of\u00a0 \u00a0 log7018 in terms of\u00a0 a \u00a0 and\u00a0 b \u00a0. Q6.\u00a0Solve for\u00a0 [&hellip;]<!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt -->","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-548","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\/548","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\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=548"}],"version-history":[{"count":27,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/548\/revisions"}],"predecessor-version":[{"id":2190,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/548\/revisions\/2190"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=548"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}