Answer Key 11.5

  1. 9^2=81
  2. b^{-16}=a
  3. \left(\dfrac{1}{49}\right)^{-2}=7
  4. 16^2=256
  5. 13^2=169
  6. 11^0=1
  7. \log_{8}1=0
  8. \log_{17}\dfrac{1}{289}=-2
  9. \log_{15}225=2
  10. \log_{144}12=\dfrac{1}{2}
  11. \log_{64}2=\dfrac{1}{6}
  12. \log_{19}361=2
  13. \begin{array}{rrl} \\ \\ \\ \\ \\ \log_{125}5&=&x \\ 125^x&=&5 \\ 5^{3x}&=&5 \\ 3x&=&1 \\ \\ x&=&\dfrac{1}{3} \end{array}
  14. \begin{array}{rrl} \\ \\ \\ \log_{5}125&=&x \\ 5^x&=&125 \\ 5^x&=&5^3 \\ x&=&3 \end{array}
  15. \begin{array}{rrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ \log_{343}\dfrac{1}{7}&=&x \\ \\ 343^x&=&\dfrac{1}{7} \\ \\ 7^{3x}&=&7^{-1} \\ \\ 3x&=&-1 \\ \\ x&=&-\dfrac{1}{3} \end{array}
  16. \begin{array}{rrl} \\ \\ \\ \log_{7}1&=&x \\ 7^x&=&1 \\ 7^x&=&7^0 \\ x&=&0 \end{array}
  17. \begin{array}{rrl} \\ \\ \\ \log_{4}16&=&x \\ 4^x&=&16 \\ 4^x&=&4^2 \\ x&=&2 \end{array}
  18. \begin{array}{rrl} \\ \\ \\ \\ \\ \\ \log_{4} \dfrac{1}{64}&=&x \\ \\ 4^x&=&\dfrac{1}{64} \\ \\ 4^x&=&4^{-3} \\ x&=& -3 \end{array}
  19. \begin{array}{rrl} \\ \\ \\ \log_{6}36&=&x \\ 6^x&=&36 \\ 6^x&=&6^2 \\ x&=& 2 \end{array}
  20. \begin{array}{rrl} \\ \\ \\ \\ \\ \\ \log_{36}6&=&x \\ 36^x&=&6 \\ 6^{2x}&=&6^1 \\ 2x&=&1 \\ \\ x&=& \dfrac{1}{2} \end{array}
  21. \begin{array}{rrl} \\ \\ \\ \log_{2}64&=&x \\ 2^x&=&64 \\ 2^x&=&2^6 \\ x&=& 6 \end{array}
  22. \begin{array}{rrl} \\ \\ \\ \log_{3}243 &=&x \\ 3^x&=&243 \\ 3^x&=&3^5 \\ x&=&5 \end{array}
  23. \begin{array}{rrl} \\ 5^1&=& x \\ x&=&5 \end{array}
  24. \begin{array}{rrl} \\ 8^3&=& k \\ k&=&512 \end{array}
  25. \begin{array}{rrl} \\ \\ 2^{-2}&=&x \\ \\ x&=&\dfrac{1}{4} \end{array}
  26. \begin{array}{rrl} \\ 10^3&=& \\ n&=&1000 \end{array}
  27. \begin{array}{rrl} \\ 11^2&=&k \\ k&=&121 \end{array}
  28. \begin{array}{rrl} \\ 4^4&=& p \\ p&=&256 \end{array}
  29. \begin{array}{rrrrr} \\ \\ \\ \\ 9^4&=&n&+&9 \\ -9&&&-&9 \\ \midrule n&=&9^4&-&9 \\ n&=&6561&-&9 \\ n&=&6552&& \end{array}
  30. \begin{array}{rrrrr} \\ \\ \\ \\ \\ 11^{-1}&=&x&-&4 \\ +4&&&+&4 \\ \midrule x&=&4&+&\dfrac{1}{11} \\ \\ x&=&4\dfrac{1}{11}&& \end{array}
  31. \begin{array}{rrl} \\ \\ \\ \\ \\ 5^3&=&-3m \\ \\ m&=&\dfrac{5^3}{-3} \\ \\ m&=&-\dfrac{125}{3} \end{array}
  32. \begin{array}{rrl} \\ \\ 2^1&=&-8r \\ \\ r&=&\dfrac{2}{-8} \Rightarrow -\dfrac{1}{4} \end{array}
  33. \begin{array}{rrrrl} \\ \\ \\ \\ \\ 11^{-1}&=&x&+&5 \\ -5&&&-&5 \\ \midrule x&=&-5&+&\dfrac{1}{11} \\ \\ x&=&-4\dfrac{10}{11}&& \end{array}
  34. \begin{array}{rrl} \\ \\ \\ \\ \\ 7^4&=&-3n \\ \\ n&=&\dfrac{7^4}{-3} \\ \\ n&=&-\dfrac{2401}{3} \end{array}
  35. \begin{array}{rrrrr} \\ \\ \\ \\ \\ \\ 4^0&=&6b&+&4 \\ -4&&&-&4 \\ \midrule 6b&=&-4&+&1 \\ 6b&=&-3&& \\ \\ b&=&-\dfrac{1}{2}&& \end{array}
  36. \begin{array}{rrrrr} \\ \\ \\ \\ \\ \\ \\ \\ 11^{-1}&=&10v&+&1 \\ -1&&&-&1 \\ \midrule 10v&=&-1&+&\dfrac{1}{11} \\ \\ 10v&=&-\dfrac{10}{11}&& \\ \\ v&=&-\dfrac{1}{11} \end{array}
  37. \begin{array}{rrrrr} \\ \\ \\ \\ \\ \\ \\ 5^4&=&-10x&+&4 \\ 625&=&-10x&+&4 \\ -4&&&-&4 \\ \midrule \dfrac{621}{-10}&=&\dfrac{-10x}{-10}&& \\ \\ x&=&-\dfrac{621}{10}&& \\ \end{array}
  38. \begin{array}{rrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 9^{-2}&=&7&-&6x \\ -7&&-7&& \\ \midrule -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}
  39. \begin{array}{rrrrr} \\ \\ \\ \\ \\ \\ 2^3&=&10&-&5a \\ -10&&-10&& \\ \midrule -5a&=&8&-&10 \\ -5a&=&-2&& \\ \\ a&=&\dfrac{2}{5}&& \end{array}
  40. \begin{array}{rrlrr} \\ \\ \\ 8&=&3k&-&1 \\ +1&&&+&1 \\ \midrule 9&=&3k&& \\ k&=&3&& \end{array}

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Intermediate Algebra by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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