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. $\log_{125}5=x$
$\begin{array}[t]{rrl}125^x&=&5 \\ 5^{3x}&=&5 \\ 3x&=&1 \\ \\ x&=&\dfrac{1}{3} \end{array}$
14. $\log_{5}125=x$
$\begin{array}[t]{rrl} \phantom{log}5^x&=&125 \\ 5^x&=&5^3 \\ x&=&3 \end{array}$
15. $\log_{343}\dfrac{1}{7}=x$
$\begin{array}[t]{rrl} \phantom{lo}343^x&=&\dfrac{1}{7} \\ \\ 7^{3x}&=&7^{-1} \\ \\ 3x&=&-1 \\ \\ x&=&-\dfrac{1}{3} \end{array}$
16. $\log_{7}1=x$
$\begin{array}[t]{rrl} \phantom{lo}7^x&=&1 \\ 7^x&=&7^0 \\ x&=&0 \end{array}$
17. $\log_{4}16=x$
$\begin{array}[t]{rrl} \phantom{log}4^x&=&16 \\ 4^x&=&4^2 \\ x&=&2 \end{array}$
18. $\log_{4} \dfrac{1}{64}=x$
$\begin{array}[t]{rrl} \phantom{log}4^x&=&\dfrac{1}{64} \\ \\ 4^x&=&4^{-3} \\ x&=& -3 \end{array}$
19. $\log_{6}36=x$
$\begin{array}[t]{rrl} \phantom{log}6^x&=&36 \\ 6^x&=&6^2 \\ x&=& 2 \end{array}$
20. $\log_{36}6=x$
$\begin{array}[t]{rrl} \phantom{l}36^x&=&6 \\ 6^{2x}&=&6^1 \\ 2x&=&1 \\ \\ x&=& \dfrac{1}{2} \end{array}$
21. $\log_{2}64=x$
$\begin{array}[t]{rrl} \phantom{llo}2^x&=&64 \\ 2^x&=&2^6 \\ x&=& 6 \end{array}$
22. $\log_{3}243=x$
$\begin{array}[t]{rrl} \phantom{llog}3^x&=&243 \\ 3^x&=&3^5 \\ x&=&5 \end{array}$
23. $5^1=x$
$x=5$
24. $8^3=k$
$k=512$
25. $2^{-2}=x$
$x=\dfrac{1}{4}$
26. $10^3=$
$\quad n=1000$
27. $11^2=k$
$k=121$
28. $4^4=p$
$p=256$
29. $\phantom{a}$
$\begin{array}[t]{rrrrr} 9^4&=&n&+&9 \\ -9&&&-&9 \\ \hline n&=&9^4&-&9 \\ n&=&6561&-&9 \\ n&=&6552&& \end{array}$
30. $\phantom{a}$
$\begin{array}[t]{rrrrr} 11^{-1}&=&x&-&4 \\ +4&&&+&4 \\ \hline x&=&4&+&\dfrac{1}{11} \\ \\ x&=&4\dfrac{1}{11}&& \end{array}$
31. $5^3=-3m$
$m=\dfrac{5^3}{-3}$
$m=-\dfrac{125}{3}$
32. $2^1=-8r$
$r=\dfrac{2}{-8} \Rightarrow -\dfrac{1}{4}$
33. $\phantom{a}$
$\begin{array}[t]{rrrrl} 11^{-1}&=&x&+&5 \\ -5&&&-&5 \\ \hline x&=&-5&+&\dfrac{1}{11} \\ \\ x&=&-4\dfrac{10}{11}&& \end{array}$
34. $7^4=-3n$
$n=\dfrac{7^4}{-3}$
$n=-\dfrac{2401}{3}$
35. $\phantom{a}$
$\begin{array}[t]{rrrrr} 4^0&=&6b&+&4 \\ -4&&&-&4 \\ \hline 6b&=&-4&+&1 \\ 6b&=&-3&& \\ \\ b&=&-\dfrac{1}{2}&& \end{array}$
36. $\phantom{a}$
$\begin{array}[t]{rrrrr} 11^{-1}&=&10v&+&1 \\ -1&&&-&1 \\ \hline 10v&=&-1&+&\dfrac{1}{11} \\ \\ 10v&=&-\dfrac{10}{11}&& \\ \\ v&=&-\dfrac{1}{11} \end{array}$
37. $\phantom{a}$
$\begin{array}[t]{rrrrr} 5^4&=&-10x&+&4 \\ 625&=&-10x&+&4 \\ -4&&&-&4 \\ \hline \dfrac{621}{-10}&=&\dfrac{-10x}{-10}&& \\ \\ x&=&-\dfrac{621}{10}&& \\ \end{array}$
38. $\phantom{a}$
$\begin{array}[t]{rrrrr} 9^{-2}&=&7&-&6x \\ -7&&-7&& \\ \hline -6x&=&-7&+&\dfrac{1}{81} \\ \\ -6x&=&-\dfrac{566}{81}&& \\ \\ x&=&\dfrac{566}{81\cdot 6}&& \\ \\ x&=&\dfrac{566}{486}&& \\ \\ x&=&\dfrac{283}{243}&& \end{array}$
39. $\phantom{a}$
$\begin{array}[t]{rrrrr} 2^3&=&10&-&5a \\ -10&&-10&& \\ \hline -5a&=&8&-&10 \\ -5a&=&-2&& \\ \\ a&=&\dfrac{2}{5}&& \end{array}$
40. $\phantom{a}$
$\begin{array}[t]{rrlrr} 8&=&3k&-&1 \\ +1&&&+&1 \\ \hline 9&=&3k&& \\ k&=&3&& \end{array}$