Answer Key 11.5
- [latex]9^2=81[/latex]
- [latex]b^{-16}=a[/latex]
- [latex]\left(\dfrac{1}{49}\right)^{-2}=7[/latex]
- [latex]16^2=256[/latex]
- [latex]13^2=169[/latex]
- [latex]11^0=1[/latex]
- [latex]\log_{8}1=0[/latex]
- [latex]\log_{17}\dfrac{1}{289}=-2[/latex]
- [latex]\log_{15}225=2[/latex]
- [latex]\log_{144}12=\dfrac{1}{2}[/latex]
- [latex]\log_{64}2=\dfrac{1}{6}[/latex]
- [latex]\log_{19}361=2[/latex]
- [latex]\log_{125}5=x[/latex]
[latex]\begin{array}[t]{rrl}125^x&=&5 \\ 5^{3x}&=&5 \\ 3x&=&1 \\ \\ x&=&\dfrac{1}{3} \end{array}[/latex] - [latex]\log_{5}125=x[/latex]
[latex]\begin{array}[t]{rrl} \phantom{log}5^x&=&125 \\ 5^x&=&5^3 \\ x&=&3 \end{array}[/latex] - [latex]\log_{343}\dfrac{1}{7}=x[/latex]
[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] - [latex]\log_{7}1=x[/latex]
[latex]\begin{array}[t]{rrl} \phantom{lo}7^x&=&1 \\ 7^x&=&7^0 \\ x&=&0 \end{array}[/latex] - [latex]\log_{4}16=x[/latex]
[latex]\begin{array}[t]{rrl} \phantom{log}4^x&=&16 \\ 4^x&=&4^2 \\ x&=&2 \end{array}[/latex] - [latex]\log_{4} \dfrac{1}{64}=x[/latex]
[latex]\begin{array}[t]{rrl} \phantom{log}4^x&=&\dfrac{1}{64} \\ \\ 4^x&=&4^{-3} \\ x&=& -3 \end{array}[/latex] - [latex]\log_{6}36=x[/latex]
[latex]\begin{array}[t]{rrl} \phantom{log}6^x&=&36 \\ 6^x&=&6^2 \\ x&=& 2 \end{array}[/latex] - [latex]\log_{36}6=x[/latex]
[latex]\begin{array}[t]{rrl} \phantom{l}36^x&=&6 \\ 6^{2x}&=&6^1 \\ 2x&=&1 \\ \\ x&=& \dfrac{1}{2} \end{array}[/latex] - [latex]\log_{2}64=x[/latex]
[latex]\begin{array}[t]{rrl} \phantom{llo}2^x&=&64 \\ 2^x&=&2^6 \\ x&=& 6 \end{array}[/latex] - [latex]\log_{3}243=x[/latex]
[latex]\begin{array}[t]{rrl} \phantom{llog}3^x&=&243 \\ 3^x&=&3^5 \\ x&=&5 \end{array}[/latex] - [latex]5^1=x[/latex]
[latex]x=5[/latex] - [latex]8^3=k[/latex]
[latex]k=512[/latex] - [latex]2^{-2}=x[/latex]
[latex]x=\dfrac{1}{4}[/latex] - [latex]10^3=[/latex]
[latex]\quad n=1000[/latex] - [latex]11^2=k[/latex]
[latex]k=121[/latex] - [latex]4^4=p[/latex]
[latex]p=256[/latex] - [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{rrrrr} 9^4&=&n&+&9 \\ -9&&&-&9 \\ \hline n&=&9^4&-&9 \\ n&=&6561&-&9 \\ n&=&6552&& \end{array}[/latex] - [latex]\phantom{a}[/latex]
[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] - [latex]5^3=-3m[/latex]
[latex]m=\dfrac{5^3}{-3}[/latex]
[latex]m=-\dfrac{125}{3}[/latex] - [latex]2^1=-8r[/latex]
[latex]r=\dfrac{2}{-8} \Rightarrow -\dfrac{1}{4}[/latex] - [latex]\phantom{a}[/latex]
[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] - [latex]7^4=-3n[/latex]
[latex]n=\dfrac{7^4}{-3}[/latex]
[latex]n=-\dfrac{2401}{3}[/latex] - [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{rrrrr} 4^0&=&6b&+&4 \\ -4&&&-&4 \\ \hline 6b&=&-4&+&1 \\ 6b&=&-3&& \\ \\ b&=&-\dfrac{1}{2}&& \end{array}[/latex] - [latex]\phantom{a}[/latex]
[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] - [latex]\phantom{a}[/latex]
[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] - [latex]\phantom{a}[/latex]
[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] - [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{rrrrr} 2^3&=&10&-&5a \\ -10&&-10&& \\ \hline -5a&=&8&-&10 \\ -5a&=&-2&& \\ \\ a&=&\dfrac{2}{5}&& \end{array}[/latex] - [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{rrlrr} 8&=&3k&-&1 \\ +1&&&+&1 \\ \hline 9&=&3k&& \\ k&=&3&& \end{array}[/latex]
