{"id":8544,"date":"2013-10-28T20:41:20","date_gmt":"2013-10-28T12:41:20","guid":{"rendered":"http:\/\/www.intmath.com\/blog\/?p=8544"},"modified":"2018-01-29T18:34:52","modified_gmt":"2018-01-29T10:34:52","slug":"intmath-newsletter-solving-log-equations-graphs","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/letters\/intmath-newsletter-solving-log-equations-graphs-8544","title":{"rendered":"IntMath Newsletter: Solving log equations, graphs"},"content":{"rendered":"<p>28 Oct 2013 <\/p>\n<p>In this Newsletter:<\/p>\n<p>1. When does <span class=\"intmath\">log(<em>x <\/em>&minus; 3) = log <em>x<\/em> &minus; log 3<\/span>?<br \/>\n2. Updated math interactives <br \/>\n3. IntMath poll <br \/>\n4.  Math puzzles <br \/>\n5. Friday math movie - Smart failure <br \/>\n6. Final thought - Learning to learn <\/p>\n<h2>1. When does log(<em>x<\/em>-3) = log <em>x<\/em> - log 3?<\/h2>\n<table border=\"0\" cellpadding=\"5\">\n<tbody>\n<tr>\n<td><a href=\"https:\/\/www.intmath.com\/blog\/mathematics\/when-does-logx-3-log-x-log-3-8535\"><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2013\/10\/log_th4.png\" alt=\"intersecting log curves\" height=\"100\" width=\"128\" \/><\/a><\/td>\n<td>\n<p> A recent comment from a Twitter colleague got me thinking about the value of graphical solutions of equations.<\/p>\n<p><a href=\"https:\/\/www.intmath.com\/blog\/mathematics\/when-does-logx-3-log-x-log-3-8535\"> When does log(<em>x<\/em>-3) = log <em>x<\/em> - log 3?<\/a><\/p>\n<p>Do you agree with me?<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>2. Updated math interactives<\/h2>\n<p>These are the latest conversions I've done from Flash to mobile-friendly javascript. <\/p>\n<p><strong>a. Mortgage calculator with graph <\/strong><\/p>\n<table border=\"0\" cellpadding=\"5\">\n<tbody>\n<tr>\n<td><a href=\"https:\/\/www.intmath.com\/money-math\/3-math-of-house-buying.php#mortgage_interactive\"><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2013\/10\/mortgage-applet2.png\" alt=\"mortgage calculator and graph\" width=\"128\" height=\"100\" \/><\/a><\/td>\n<td>\n<p> The most expensive thing most people buy is a house. It's a good idea to know what will happen when it comes to the mortgage you'll be paying back for much of your working life. <\/p>\n<p><a href=\"https:\/\/www.intmath.com\/money-math\/3-math-of-house-buying.php#mortgage_interactive\"> Interactive mortgage calculator <\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>b.<\/strong> <strong>Graphing calculator<\/strong> <\/p>\n<table border=\"0\" cellpadding=\"5\">\n<tbody>\n<tr>\n<td><a href=\"https:\/\/www.intmath.com\/functions-and-graphs\/graphs-using-svg.php\"><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2012\/02\/svg-graph.png\" alt=\"Plot your own graph using SVG\" width=\"128\" height=\"100\" \/><\/a><\/td>\n<td>\n<p> You can now save a link to any graph you produce with this calculator. (After you've created your own graph and sized it how you like, a link will appear which you can include in an email or wherever.) <\/p>\n<p><a href=\"https:\/\/www.intmath.com\/functions-and-graphs\/graphs-using-svg.php\">Graphing Calculator (SVG)<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>3. IntMath Poll<\/h2>\n<p>The  IntMath Poll during Sep\/Oct asked readers:<\/p>\n<p><strong>Generally, how do you feel about school?<\/strong><\/p>\n<p>It's sad that for many students, school is not a happy place. At least the majority of respondents said either they like it or are neutral.<\/p>\n<p>I hate it and can&rsquo;t wait to finish  28%<\/p>\n<p>I really love school  26%<\/p>\n<p>It&rsquo;s OK  22%<\/p>\n<p>I enjoy it  18%<\/p>\n<p>I don&rsquo;t like it  6%<\/p>\n<p>Total votes: <strong>3100<\/strong><\/p>\n<p><strong>Current IntMath Poll: <\/strong>With so many students unhappy at school, how can we improve it? You can give your opinion on any (inner) page of  <a href=\"https:\/\/www.intmath.com\/\">IntMath.com<\/a>.<\/p>\n<h2>4. Math puzzles<\/h2>\n<p>The <a href=\"https:\/\/www.intmath.com\/blog\/letters\/intmath-newsletter-resources-primes-matrix-app-and-role-models-8512#puzzle\">puzzle in the last IntMath Newsletter<\/a> asked about the sum of an infinite series.<\/p>\n<p>Correct <a href=\"https:\/\/www.intmath.com\/blog\/letters\/intmath-newsletter-resources-primes-matrix-app-and-role-models-8512#comments\">answers with explanation<\/a> were given by  Tomas, Don and Mawanda but my vote for the clearest answer is Mawanda's.<\/p>\n<p id=\"puzzle\"><strong>New math puzzle<\/strong><\/p>\n<p>Find the least 2 positive integers having the remainders 2, 3, 2 when divided by 3, 5, 7 respectively. <\/p>\n<p>Leave your responses <a href=\"https:\/\/www.intmath.com\/blog\/letters\/intmath-newsletter-solving-log-equations-graphs-8544#respond\">here<\/a>. <\/p>\n<h2>5. Friday math movie: Smart failure for a fast-changing world<\/h2>\n<table border=\"0\" cellpadding=\"5\">\n<tbody>\n<tr>\n<td><a href=\"https:\/\/www.intmath.com\/blog\/videos\/friday-math-movie-smart-failure-for-a-fast-changing-world-7591\"><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2013\/07\/smart-failure.jpg\" alt=\"Smart failure\" height=\"100\" width=\"128\" \/><\/a><\/td>\n<td>\n<p> We don't deal with failure properly in most educational settings. This talk gives some options for improving that.<\/p>\n<p><a href=\"https:\/\/www.intmath.com\/blog\/videos\/friday-math-movie-smart-failure-for-a-fast-changing-world-7591\"> Friday math movie: Smart failure for a fast-changing world<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>6. Final thought: Learning to learn <\/h2>\n<p>Most teachers (and parents) tell students to &quot;study hard&quot;. But even though some students put a lot of time into study, some produce better outcomes than others.<\/p>\n<p>In <a href=\"http:\/\/link.springer.com\/article\/10.1007%2Fs11251-011-9182-5\">a 2011 study<\/a>, researchers found that if students knew more about their own learning approach, the more likely they were to do well.  Also, those who used a variety of learning strategies did better than those who stuck to one or two. <\/p>\n<p>How many of the following successful learning strategies can you say &quot;yes&quot; to? <\/p>\n<ul>\n<li>I draw pictures or diagrams to help me understand.<\/li>\n<li> I make up questions that I try to answer.<\/li>\n<li>When I am learning something new, I think back to what I already know about it.<\/li>\n<li> I discuss what I am learning with others.<\/li>\n<li> I practice things over and over until I know them well.<\/li>\n<li> I think about my thinking, to check if I understand the idea.<\/li>\n<li> When I don't understand something I go back over it again.<\/li>\n<li> I make a note of things that I don't understand very wel, so that I can follow them up.<\/li>\n<li> When I have finished an activity I look back to see how well I did.<\/li>\n<li> I organize my time to manage my learning.<\/li>\n<li> I make plans for how to do the activities.<\/li>\n<\/ul>\n<p>For the ones you said &quot;no&quot; to, why not give them a try? <\/p>\n<p>Until next time, enjoy whatever you learn.<\/p>\n<p class=\"alt\">See the <a href=\"https:\/\/www.intmath.com\/blog\/letters\/intmath-newsletter-solving-log-equations-graphs-8544#comments\" id=\"comms\">5 Comments<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this Newsletter:<\/p>\n<p>1. When does <span class=\"math\">log(<em>x <\/em>&minus; 3) = log <em>x<\/em> &minus; log 3<\/span>?<br \/>\n2. Updated math interactives <br \/>\n3. IntMath poll <br \/>\n4.  Math puzzles <br \/>\n5. Friday math movie - Smart failure <br \/>\n6. Final thought - Learning to learn <\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mo_disable_npp":""},"categories":[104],"tags":[],"_links":{"self":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/8544"}],"collection":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/comments?post=8544"}],"version-history":[{"count":1,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/8544\/revisions"}],"predecessor-version":[{"id":11397,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/8544\/revisions\/11397"}],"wp:attachment":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/media?parent=8544"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/categories?post=8544"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/tags?post=8544"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}