{"id":1838,"date":"2019-08-15T14:01:39","date_gmt":"2019-08-15T18:01:39","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1838"},"modified":"2019-08-15T16:18:58","modified_gmt":"2019-08-15T20:18:58","slug":"answer-key-11-5","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-11-5\/","title":{"raw":"Answer Key 11.5","rendered":"Answer Key 11.5"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(9^2=81\\)<\/li>\r\n \t
  2. \\(b^{-16}=a\\)<\/li>\r\n \t
  3. \\(\\left(\\dfrac{1}{49}\\right)^{-2}=7\\)<\/li>\r\n \t
  4. \\(16^2=256\\)<\/li>\r\n \t
  5. \\(13^2=169\\)<\/li>\r\n \t
  6. \\(11^0=1\\)<\/li>\r\n \t
  7. \\(\\log_{8}1=0\\)<\/li>\r\n \t
  8. \\(\\log_{17}\\dfrac{1}{289}=-2\\)<\/li>\r\n \t
  9. \\(\\log_{15}225=2\\)<\/li>\r\n \t
  10. \\(\\log_{144}12=\\dfrac{1}{2}\\)<\/li>\r\n \t
  11. \\(\\log_{64}2=\\dfrac{1}{6}\\)<\/li>\r\n \t
  12. \\(\\log_{19}361=2\\)<\/li>\r\n \t
  13. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\log_{125}5&=&x \\\\\r\n125^x&=&5 \\\\\r\n5^{3x}&=&5 \\\\\r\n3x&=&1 \\\\ \\\\\r\nx&=&\\dfrac{1}{3}\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\n\\log_{5}125&=&x \\\\\r\n5^x&=&125 \\\\\r\n5^x&=&5^3 \\\\\r\nx&=&3\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\log_{343}\\dfrac{1}{7}&=&x \\\\ \\\\\r\n343^x&=&\\dfrac{1}{7} \\\\ \\\\\r\n7^{3x}&=&7^{-1} \\\\ \\\\\r\n3x&=&-1 \\\\ \\\\\r\nx&=&-\\dfrac{1}{3}\r\n\\end{array}\\)<\/li>\r\n \t
  16. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\n\\log_{7}1&=&x \\\\\r\n7^x&=&1 \\\\\r\n7^x&=&7^0 \\\\\r\nx&=&0\r\n\\end{array}\\)<\/li>\r\n \t
  17. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\n\\log_{4}16&=&x \\\\\r\n4^x&=&16 \\\\\r\n4^x&=&4^2 \\\\\r\nx&=&2\r\n\\end{array}\\)<\/li>\r\n \t
  18. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\log_{4} \\dfrac{1}{64}&=&x \\\\ \\\\\r\n4^x&=&\\dfrac{1}{64} \\\\ \\\\\r\n4^x&=&4^{-3} \\\\\r\nx&=& -3\r\n\\end{array}\\)<\/li>\r\n \t
  19. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\n\\log_{6}36&=&x \\\\\r\n6^x&=&36 \\\\\r\n6^x&=&6^2 \\\\\r\nx&=& 2\r\n\\end{array}\\)<\/li>\r\n \t
  20. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\log_{36}6&=&x \\\\\r\n36^x&=&6 \\\\\r\n6^{2x}&=&6^1 \\\\\r\n2x&=&1 \\\\ \\\\\r\nx&=& \\dfrac{1}{2}\r\n\\end{array}\\)<\/li>\r\n \t
  21. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\n\\log_{2}64&=&x \\\\\r\n2^x&=&64 \\\\\r\n2^x&=&2^6 \\\\\r\nx&=& 6\r\n\\end{array}\\)<\/li>\r\n \t
  22. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\n\\log_{3}243 &=&x \\\\\r\n3^x&=&243 \\\\\r\n3^x&=&3^5 \\\\\r\nx&=&5\r\n\\end{array}\\)<\/li>\r\n \t
  23. \\(\\begin{array}{rrl}\r\n\\\\\r\n5^1&=& x \\\\\r\nx&=&5\r\n\\end{array}\\)<\/li>\r\n \t
  24. \\(\\begin{array}{rrl}\r\n\\\\\r\n8^3&=& k \\\\\r\nk&=&512\r\n\\end{array}\\)<\/li>\r\n \t
  25. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n2^{-2}&=&x \\\\ \\\\\r\nx&=&\\dfrac{1}{4}\r\n\\end{array}\\)<\/li>\r\n \t
  26. \\(\\begin{array}{rrl}\r\n\\\\\r\n10^3&=& \\\\\r\nn&=&1000\r\n\\end{array}\\)<\/li>\r\n \t
  27. \\(\\begin{array}{rrl}\r\n\\\\\r\n11^2&=&k \\\\\r\nk&=&121\r\n\\end{array}\\)<\/li>\r\n \t
  28. \\(\\begin{array}{rrl}\r\n\\\\\r\n4^4&=& p \\\\\r\np&=&256\r\n\\end{array}\\)<\/li>\r\n \t
  29. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\\r\n9^4&=&n&+&9 \\\\\r\n-9&&&-&9 \\\\\r\n\\midrule\r\nn&=&9^4&-&9 \\\\\r\nn&=&6561&-&9 \\\\\r\nn&=&6552&&\r\n\\end{array}\\)<\/li>\r\n \t
  30. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n11^{-1}&=&x&-&4 \\\\\r\n+4&&&+&4 \\\\\r\n\\midrule\r\nx&=&4&+&\\dfrac{1}{11} \\\\ \\\\\r\nx&=&4\\dfrac{1}{11}&&\r\n\\end{array}\\)<\/li>\r\n \t
  31. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n5^3&=&-3m \\\\ \\\\\r\nm&=&\\dfrac{5^3}{-3} \\\\ \\\\\r\nm&=&-\\dfrac{125}{3}\r\n\\end{array}\\)<\/li>\r\n \t
  32. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n2^1&=&-8r \\\\ \\\\\r\nr&=&\\dfrac{2}{-8} \\Rightarrow -\\dfrac{1}{4}\r\n\\end{array}\\)<\/li>\r\n \t
  33. \\(\\begin{array}{rrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n11^{-1}&=&x&+&5 \\\\\r\n-5&&&-&5 \\\\\r\n\\midrule\r\nx&=&-5&+&\\dfrac{1}{11} \\\\ \\\\\r\nx&=&-4\\dfrac{10}{11}&&\r\n\\end{array}\\)<\/li>\r\n \t
  34. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n7^4&=&-3n \\\\ \\\\\r\nn&=&\\dfrac{7^4}{-3} \\\\ \\\\\r\nn&=&-\\dfrac{2401}{3}\r\n\\end{array}\\)<\/li>\r\n \t
  35. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n4^0&=&6b&+&4 \\\\\r\n-4&&&-&4 \\\\\r\n\\midrule\r\n6b&=&-4&+&1 \\\\\r\n6b&=&-3&& \\\\ \\\\\r\nb&=&-\\dfrac{1}{2}&&\r\n\\end{array}\\)<\/li>\r\n \t
  36. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n11^{-1}&=&10v&+&1 \\\\\r\n-1&&&-&1 \\\\\r\n\\midrule\r\n10v&=&-1&+&\\dfrac{1}{11} \\\\ \\\\\r\n10v&=&-\\dfrac{10}{11}&& \\\\ \\\\\r\nv&=&-\\dfrac{1}{11}\r\n\\end{array}\\)<\/li>\r\n \t
  37. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n5^4&=&-10x&+&4 \\\\\r\n625&=&-10x&+&4 \\\\\r\n-4&&&-&4 \\\\\r\n\\midrule\r\n\\dfrac{621}{-10}&=&\\dfrac{-10x}{-10}&& \\\\ \\\\\r\nx&=&-\\dfrac{621}{10}&& \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  38. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n9^{-2}&=&7&-&6x \\\\\r\n-7&&-7&& \\\\\r\n\\midrule\r\n-6x&=&-7&+&\\dfrac{1}{81} \\\\ \\\\\r\n-6x&=&-\\dfrac{566}{81}&& \\\\ \\\\\r\nx&=&\\dfrac{566}{81\\cdot 6}&& \\\\ \\\\\r\nx&=&\\dfrac{566}{486}&& \\\\ \\\\\r\nx&=&\\dfrac{283}{243}&&\r\n\\end{array}\\)<\/li>\r\n \t
  39. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n2^3&=&10&-&5a \\\\\r\n-10&&-10&& \\\\\r\n\\midrule\r\n-5a&=&8&-&10 \\\\\r\n-5a&=&-2&& \\\\ \\\\\r\na&=&\\dfrac{2}{5}&&\r\n\\end{array}\\)<\/li>\r\n \t
  40. \\(\\begin{array}{rrlrr}\r\n\\\\ \\\\ \\\\\r\n8&=&3k&-&1 \\\\\r\n+1&&&+&1 \\\\\r\n\\midrule\r\n9&=&3k&& \\\\\r\nk&=&3&&\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
      \n
    1. \"9^2=81\"<\/li>\n
    2. \"b^{-16}=a\"<\/li>\n
    3. \"\left(\dfrac{1}{49}\right)^{-2}=7\"<\/li>\n
    4. \"16^2=256\"<\/li>\n
    5. \"13^2=169\"<\/li>\n
    6. \"11^0=1\"<\/li>\n
    7. \"\log_{8}1=0\"<\/li>\n
    8. \"\log_{17}\dfrac{1}{289}=-2\"<\/li>\n
    9. \"\log_{15}225=2\"<\/li>\n
    10. \"\log_{144}12=\dfrac{1}{2}\"<\/li>\n
    11. \"\log_{64}2=\dfrac{1}{6}\"<\/li>\n
    12. \"\log_{19}361=2\"<\/li>\n
    13. \"\begin{array}{rrl}<\/li>\n
    14. \"\begin{array}{rrl}<\/li>\n
    15. \"\begin{array}{rrl}<\/li>\n
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    27. \"\begin{array}{rrl}<\/li>\n
    28. \"\begin{array}{rrl}<\/li>\n
    29. \"\begin{array}{rrrrr}<\/li>\n
    30. \"\begin{array}{rrrrr}<\/li>\n
    31. \"\begin{array}{rrl}<\/li>\n
    32. \"\begin{array}{rrl}<\/li>\n
    33. \"\begin{array}{rrrrl}<\/li>\n
    34. \"\begin{array}{rrl}<\/li>\n
    35. \"\begin{array}{rrrrr}<\/li>\n
    36. \"\begin{array}{rrrrr}<\/li>\n
    37. \"\begin{array}{rrrrr}<\/li>\n
    38. \"\begin{array}{rrrrr}<\/li>\n
    39. \"\begin{array}{rrrrr}<\/li>\n
    40. \"\begin{array}{rrlrr}<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":106,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1838","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1838","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/727"}],"version-history":[{"count":5,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1838\/revisions"}],"predecessor-version":[{"id":1843,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1838\/revisions\/1843"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1838\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1838"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1838"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1838"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1838"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}