{"id":2024,"date":"2021-12-02T19:40:32","date_gmt":"2021-12-03T00:40:32","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-11-5\/"},"modified":"2023-09-01T15:01:15","modified_gmt":"2023-09-01T19:01:15","slug":"answer-key-11-5","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-11-5\/","title":{"raw":"Answer Key 11.5","rendered":"Answer Key 11.5"},"content":{"raw":"
    \r\n \t
  1. [latex]9^2=81[\/latex]<\/li>\r\n \t
  2. [latex]b^{-16}=a[\/latex]<\/li>\r\n \t
  3. [latex]\\left(\\dfrac{1}{49}\\right)^{-2}=7[\/latex]<\/li>\r\n \t
  4. [latex]16^2=256[\/latex]<\/li>\r\n \t
  5. [latex]13^2=169[\/latex]<\/li>\r\n \t
  6. [latex]11^0=1[\/latex]<\/li>\r\n \t
  7. [latex]\\log_{8}1=0[\/latex]<\/li>\r\n \t
  8. [latex]\\log_{17}\\dfrac{1}{289}=-2[\/latex]<\/li>\r\n \t
  9. [latex]\\log_{15}225=2[\/latex]<\/li>\r\n \t
  10. [latex]\\log_{144}12=\\dfrac{1}{2}[\/latex]<\/li>\r\n \t
  11. [latex]\\log_{64}2=\\dfrac{1}{6}[\/latex]<\/li>\r\n \t
  12. [latex]\\log_{19}361=2[\/latex]<\/li>\r\n \t
  13. [latex]\\log_{125}5=x[\/latex]\r\n[latex]\\begin{array}[t]{rrl}125^x&=&5 \\\\\r\n5^{3x}&=&5 \\\\\r\n3x&=&1 \\\\ \\\\\r\nx&=&\\dfrac{1}{3}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  14. [latex]\\log_{5}125=x[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\phantom{log}5^x&=&125 \\\\\r\n5^x&=&5^3 \\\\\r\nx&=&3\r\n\\end{array}[\/latex]<\/li>\r\n \t
  15. [latex]\\log_{343}\\dfrac{1}{7}=x [\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\phantom{lo}343^x&=&\\dfrac{1}{7} \\\\ \\\\\r\n7^{3x}&=&7^{-1} \\\\ \\\\\r\n3x&=&-1 \\\\ \\\\\r\nx&=&-\\dfrac{1}{3}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  16. [latex]\\log_{7}1=x[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\phantom{lo}7^x&=&1 \\\\\r\n7^x&=&7^0 \\\\\r\nx&=&0\r\n\\end{array}[\/latex]<\/li>\r\n \t
  17. [latex]\\log_{4}16=x [\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\phantom{log}4^x&=&16 \\\\\r\n4^x&=&4^2 \\\\\r\nx&=&2\r\n\\end{array}[\/latex]<\/li>\r\n \t
  18. [latex]\\log_{4} \\dfrac{1}{64}=x [\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\phantom{log}4^x&=&\\dfrac{1}{64} \\\\ \\\\\r\n4^x&=&4^{-3} \\\\\r\nx&=& -3\r\n\\end{array}[\/latex]<\/li>\r\n \t
  19. [latex]\\log_{6}36=x [\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\phantom{log}6^x&=&36 \\\\\r\n6^x&=&6^2 \\\\\r\nx&=& 2\r\n\\end{array}[\/latex]<\/li>\r\n \t
  20. [latex]\\log_{36}6=x[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\phantom{l}36^x&=&6 \\\\\r\n6^{2x}&=&6^1 \\\\\r\n2x&=&1 \\\\ \\\\\r\nx&=& \\dfrac{1}{2}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  21. [latex]\\log_{2}64=x[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\phantom{llo}2^x&=&64 \\\\\r\n2^x&=&2^6 \\\\\r\nx&=& 6\r\n\\end{array}[\/latex]<\/li>\r\n \t
  22. [latex]\\log_{3}243=x [\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\phantom{llog}3^x&=&243 \\\\\r\n3^x&=&3^5 \\\\\r\nx&=&5\r\n\\end{array}[\/latex]<\/li>\r\n \t
  23. [latex]5^1=x[\/latex]\r\n[latex]x=5[\/latex]<\/li>\r\n \t
  24. [latex]8^3=k[\/latex]\r\n[latex]k=512[\/latex]<\/li>\r\n \t
  25. [latex]2^{-2}=x[\/latex]\r\n[latex]x=\\dfrac{1}{4}[\/latex]<\/li>\r\n \t
  26. [latex]10^3=[\/latex]\r\n[latex]\\quad n=1000[\/latex]<\/li>\r\n \t
  27. [latex]11^2=k[\/latex]\r\n[latex]k=121[\/latex]<\/li>\r\n \t
  28. [latex]4^4=p[\/latex]\r\n[latex]p=256[\/latex]<\/li>\r\n \t
  29. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n9^4&=&n&+&9 \\\\\r\n-9&&&-&9 \\\\\r\n\\hline\r\nn&=&9^4&-&9 \\\\\r\nn&=&6561&-&9 \\\\\r\nn&=&6552&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  30. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n11^{-1}&=&x&-&4 \\\\\r\n+4&&&+&4 \\\\\r\n\\hline\r\nx&=&4&+&\\dfrac{1}{11} \\\\ \\\\\r\nx&=&4\\dfrac{1}{11}&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  31. [latex]5^3=-3m[\/latex]\r\n[latex]m=\\dfrac{5^3}{-3}[\/latex]\r\n[latex]m=-\\dfrac{125}{3}[\/latex]<\/li>\r\n \t
  32. [latex]2^1=-8r[\/latex]\r\n[latex]r=\\dfrac{2}{-8} \\Rightarrow -\\dfrac{1}{4}[\/latex]<\/li>\r\n \t
  33. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrl}\r\n11^{-1}&=&x&+&5 \\\\\r\n-5&&&-&5 \\\\\r\n\\hline\r\nx&=&-5&+&\\dfrac{1}{11} \\\\ \\\\\r\nx&=&-4\\dfrac{10}{11}&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  34. [latex]7^4=-3n[\/latex]\r\n[latex]n=\\dfrac{7^4}{-3}[\/latex]\r\n[latex]n=-\\dfrac{2401}{3}[\/latex]<\/li>\r\n \t
  35. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n4^0&=&6b&+&4 \\\\\r\n-4&&&-&4 \\\\\r\n\\hline\r\n6b&=&-4&+&1 \\\\\r\n6b&=&-3&& \\\\ \\\\\r\nb&=&-\\dfrac{1}{2}&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  36. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n11^{-1}&=&10v&+&1 \\\\\r\n-1&&&-&1 \\\\\r\n\\hline\r\n10v&=&-1&+&\\dfrac{1}{11} \\\\ \\\\\r\n10v&=&-\\dfrac{10}{11}&& \\\\ \\\\\r\nv&=&-\\dfrac{1}{11}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  37. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n5^4&=&-10x&+&4 \\\\\r\n625&=&-10x&+&4 \\\\\r\n-4&&&-&4 \\\\\r\n\\hline\r\n\\dfrac{621}{-10}&=&\\dfrac{-10x}{-10}&& \\\\ \\\\\r\nx&=&-\\dfrac{621}{10}&& \\\\\r\n\\end{array}[\/latex]<\/li>\r\n \t
  38. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n9^{-2}&=&7&-&6x \\\\\r\n-7&&-7&& \\\\\r\n\\hline\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}[\/latex]<\/li>\r\n \t
  39. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n2^3&=&10&-&5a \\\\\r\n-10&&-10&& \\\\\r\n\\hline\r\n-5a&=&8&-&10 \\\\\r\n-5a&=&-2&& \\\\ \\\\\r\na&=&\\dfrac{2}{5}&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  40. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrlrr}\r\n8&=&3k&-&1 \\\\\r\n+1&&&+&1 \\\\\r\n\\hline\r\n9&=&3k&& \\\\\r\nk&=&3&&\r\n\\end{array}[\/latex]<\/li>\r\n<\/ol>","rendered":"
      \n
    1. [latex]9^2=81[\/latex]<\/li>\n
    2. [latex]b^{-16}=a[\/latex]<\/li>\n
    3. [latex]\\left(\\dfrac{1}{49}\\right)^{-2}=7[\/latex]<\/li>\n
    4. [latex]16^2=256[\/latex]<\/li>\n
    5. [latex]13^2=169[\/latex]<\/li>\n
    6. [latex]11^0=1[\/latex]<\/li>\n
    7. [latex]\\log_{8}1=0[\/latex]<\/li>\n
    8. [latex]\\log_{17}\\dfrac{1}{289}=-2[\/latex]<\/li>\n
    9. [latex]\\log_{15}225=2[\/latex]<\/li>\n
    10. [latex]\\log_{144}12=\\dfrac{1}{2}[\/latex]<\/li>\n
    11. [latex]\\log_{64}2=\\dfrac{1}{6}[\/latex]<\/li>\n
    12. [latex]\\log_{19}361=2[\/latex]<\/li>\n
    13. [latex]\\log_{125}5=x[\/latex]
      \n[latex]\\begin{array}[t]{rrl}125^x&=&5 \\\\ 5^{3x}&=&5 \\\\ 3x&=&1 \\\\ \\\\ x&=&\\dfrac{1}{3} \\end{array}[\/latex]<\/li>\n
    14. [latex]\\log_{5}125=x[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\phantom{log}5^x&=&125 \\\\ 5^x&=&5^3 \\\\ x&=&3 \\end{array}[\/latex]<\/li>\n
    15. [latex]\\log_{343}\\dfrac{1}{7}=x[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\phantom{lo}343^x&=&\\dfrac{1}{7} \\\\ \\\\ 7^{3x}&=&7^{-1} \\\\ \\\\ 3x&=&-1 \\\\ \\\\ x&=&-\\dfrac{1}{3} \\end{array}[\/latex]<\/li>\n
    16. [latex]\\log_{7}1=x[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\phantom{lo}7^x&=&1 \\\\ 7^x&=&7^0 \\\\ x&=&0 \\end{array}[\/latex]<\/li>\n
    17. [latex]\\log_{4}16=x[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\phantom{log}4^x&=&16 \\\\ 4^x&=&4^2 \\\\ x&=&2 \\end{array}[\/latex]<\/li>\n
    18. [latex]\\log_{4} \\dfrac{1}{64}=x[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\phantom{log}4^x&=&\\dfrac{1}{64} \\\\ \\\\ 4^x&=&4^{-3} \\\\ x&=& -3 \\end{array}[\/latex]<\/li>\n
    19. [latex]\\log_{6}36=x[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\phantom{log}6^x&=&36 \\\\ 6^x&=&6^2 \\\\ x&=& 2 \\end{array}[\/latex]<\/li>\n
    20. [latex]\\log_{36}6=x[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\phantom{l}36^x&=&6 \\\\ 6^{2x}&=&6^1 \\\\ 2x&=&1 \\\\ \\\\ x&=& \\dfrac{1}{2} \\end{array}[\/latex]<\/li>\n
    21. [latex]\\log_{2}64=x[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\phantom{llo}2^x&=&64 \\\\ 2^x&=&2^6 \\\\ x&=& 6 \\end{array}[\/latex]<\/li>\n
    22. [latex]\\log_{3}243=x[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\phantom{llog}3^x&=&243 \\\\ 3^x&=&3^5 \\\\ x&=&5 \\end{array}[\/latex]<\/li>\n
    23. [latex]5^1=x[\/latex]
      \n[latex]x=5[\/latex]<\/li>\n
    24. [latex]8^3=k[\/latex]
      \n[latex]k=512[\/latex]<\/li>\n
    25. [latex]2^{-2}=x[\/latex]
      \n[latex]x=\\dfrac{1}{4}[\/latex]<\/li>\n
    26. [latex]10^3=[\/latex]
      \n[latex]\\quad n=1000[\/latex]<\/li>\n
    27. [latex]11^2=k[\/latex]
      \n[latex]k=121[\/latex]<\/li>\n
    28. [latex]4^4=p[\/latex]
      \n[latex]p=256[\/latex]<\/li>\n
    29. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} 9^4&=&n&+&9 \\\\ -9&&&-&9 \\\\ \\hline n&=&9^4&-&9 \\\\ n&=&6561&-&9 \\\\ n&=&6552&& \\end{array}[\/latex]<\/li>\n
    30. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} 11^{-1}&=&x&-&4 \\\\ +4&&&+&4 \\\\ \\hline x&=&4&+&\\dfrac{1}{11} \\\\ \\\\ x&=&4\\dfrac{1}{11}&& \\end{array}[\/latex]<\/li>\n
    31. [latex]5^3=-3m[\/latex]
      \n[latex]m=\\dfrac{5^3}{-3}[\/latex]
      \n[latex]m=-\\dfrac{125}{3}[\/latex]<\/li>\n
    32. [latex]2^1=-8r[\/latex]
      \n[latex]r=\\dfrac{2}{-8} \\Rightarrow -\\dfrac{1}{4}[\/latex]<\/li>\n
    33. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrl} 11^{-1}&=&x&+&5 \\\\ -5&&&-&5 \\\\ \\hline x&=&-5&+&\\dfrac{1}{11} \\\\ \\\\ x&=&-4\\dfrac{10}{11}&& \\end{array}[\/latex]<\/li>\n
    34. [latex]7^4=-3n[\/latex]
      \n[latex]n=\\dfrac{7^4}{-3}[\/latex]
      \n[latex]n=-\\dfrac{2401}{3}[\/latex]<\/li>\n
    35. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} 4^0&=&6b&+&4 \\\\ -4&&&-&4 \\\\ \\hline 6b&=&-4&+&1 \\\\ 6b&=&-3&& \\\\ \\\\ b&=&-\\dfrac{1}{2}&& \\end{array}[\/latex]<\/li>\n
    36. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} 11^{-1}&=&10v&+&1 \\\\ -1&&&-&1 \\\\ \\hline 10v&=&-1&+&\\dfrac{1}{11} \\\\ \\\\ 10v&=&-\\dfrac{10}{11}&& \\\\ \\\\ v&=&-\\dfrac{1}{11} \\end{array}[\/latex]<\/li>\n
    37. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} 5^4&=&-10x&+&4 \\\\ 625&=&-10x&+&4 \\\\ -4&&&-&4 \\\\ \\hline \\dfrac{621}{-10}&=&\\dfrac{-10x}{-10}&& \\\\ \\\\ x&=&-\\dfrac{621}{10}&& \\\\ \\end{array}[\/latex]<\/li>\n
    38. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} 9^{-2}&=&7&-&6x \\\\ -7&&-7&& \\\\ \\hline -6x&=&-7&+&\\dfrac{1}{81} \\\\ \\\\ -6x&=&-\\dfrac{566}{81}&& \\\\ \\\\ x&=&\\dfrac{566}{81\\cdot 6}&& \\\\ \\\\ x&=&\\dfrac{566}{486}&& \\\\ \\\\ x&=&\\dfrac{283}{243}&& \\end{array}[\/latex]<\/li>\n
    39. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} 2^3&=&10&-&5a \\\\ -10&&-10&& \\\\ \\hline -5a&=&8&-&10 \\\\ -5a&=&-2&& \\\\ \\\\ a&=&\\dfrac{2}{5}&& \\end{array}[\/latex]<\/li>\n
    40. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrlrr} 8&=&3k&-&1 \\\\ +1&&&+&1 \\\\ \\hline 9&=&3k&& \\\\ k&=&3&& \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":111,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-2024","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2024","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":2,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2024\/revisions"}],"predecessor-version":[{"id":2239,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2024\/revisions\/2239"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2024\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=2024"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=2024"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=2024"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=2024"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}