Answer Key 11.5
[latexpage]
- \(9^2=81\)
- \(b^{-16}=a\)
- \(\left(\dfrac{1}{49}\right)^{-2}=7\)
- \(16^2=256\)
- \(13^2=169\)
- \(11^0=1\)
- \(\log_{8}1=0\)
- \(\log_{17}\dfrac{1}{289}=-2\)
- \(\log_{15}225=2\)
- \(\log_{144}12=\dfrac{1}{2}\)
- \(\log_{64}2=\dfrac{1}{6}\)
- \(\log_{19}361=2\)
- \(\begin{array}{rrl}
\\ \\ \\ \\ \\
\log_{125}5&=&x \\
125^x&=&5 \\
5^{3x}&=&5 \\
3x&=&1 \\ \\
x&=&\dfrac{1}{3}
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\
\log_{5}125&=&x \\
5^x&=&125 \\
5^x&=&5^3 \\
x&=&3
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\
\log_{343}\dfrac{1}{7}&=&x \\ \\
343^x&=&\dfrac{1}{7} \\ \\
7^{3x}&=&7^{-1} \\ \\
3x&=&-1 \\ \\
x&=&-\dfrac{1}{3}
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\
\log_{7}1&=&x \\
7^x&=&1 \\
7^x&=&7^0 \\
x&=&0
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\
\log_{4}16&=&x \\
4^x&=&16 \\
4^x&=&4^2 \\
x&=&2
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\ \\ \\
\log_{4} \dfrac{1}{64}&=&x \\ \\
4^x&=&\dfrac{1}{64} \\ \\
4^x&=&4^{-3} \\
x&=& -3
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\
\log_{6}36&=&x \\
6^x&=&36 \\
6^x&=&6^2 \\
x&=& 2
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\ \\ \\
\log_{36}6&=&x \\
36^x&=&6 \\
6^{2x}&=&6^1 \\
2x&=&1 \\ \\
x&=& \dfrac{1}{2}
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\
\log_{2}64&=&x \\
2^x&=&64 \\
2^x&=&2^6 \\
x&=& 6
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\
\log_{3}243 &=&x \\
3^x&=&243 \\
3^x&=&3^5 \\
x&=&5
\end{array}\) - \(\begin{array}{rrl}
\\
5^1&=& x \\
x&=&5
\end{array}\) - \(\begin{array}{rrl}
\\
8^3&=& k \\
k&=&512
\end{array}\) - \(\begin{array}{rrl}
\\ \\
2^{-2}&=&x \\ \\
x&=&\dfrac{1}{4}
\end{array}\) - \(\begin{array}{rrl}
\\
10^3&=& \\
n&=&1000
\end{array}\) - \(\begin{array}{rrl}
\\
11^2&=&k \\
k&=&121
\end{array}\) - \(\begin{array}{rrl}
\\
4^4&=& p \\
p&=&256
\end{array}\) - \(\begin{array}{rrrrr}
\\ \\ \\ \\
9^4&=&n&+&9 \\
-9&&&-&9 \\
\midrule
n&=&9^4&-&9 \\
n&=&6561&-&9 \\
n&=&6552&&
\end{array}\) - \(\begin{array}{rrrrr}
\\ \\ \\ \\ \\
11^{-1}&=&x&-&4 \\
+4&&&+&4 \\
\midrule
x&=&4&+&\dfrac{1}{11} \\ \\
x&=&4\dfrac{1}{11}&&
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\ \\
5^3&=&-3m \\ \\
m&=&\dfrac{5^3}{-3} \\ \\
m&=&-\dfrac{125}{3}
\end{array}\) - \(\begin{array}{rrl}
\\ \\
2^1&=&-8r \\ \\
r&=&\dfrac{2}{-8} \Rightarrow -\dfrac{1}{4}
\end{array}\) - \(\begin{array}{rrrrl}
\\ \\ \\ \\ \\
11^{-1}&=&x&+&5 \\
-5&&&-&5 \\
\midrule
x&=&-5&+&\dfrac{1}{11} \\ \\
x&=&-4\dfrac{10}{11}&&
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\ \\
7^4&=&-3n \\ \\
n&=&\dfrac{7^4}{-3} \\ \\
n&=&-\dfrac{2401}{3}
\end{array}\) - \(\begin{array}{rrrrr}
\\ \\ \\ \\ \\ \\
4^0&=&6b&+&4 \\
-4&&&-&4 \\
\midrule
6b&=&-4&+&1 \\
6b&=&-3&& \\ \\
b&=&-\dfrac{1}{2}&&
\end{array}\) - \(\begin{array}{rrrrr}
\\ \\ \\ \\ \\ \\ \\ \\
11^{-1}&=&10v&+&1 \\
-1&&&-&1 \\
\midrule
10v&=&-1&+&\dfrac{1}{11} \\ \\
10v&=&-\dfrac{10}{11}&& \\ \\
v&=&-\dfrac{1}{11}
\end{array}\) - \(\begin{array}{rrrrr}
\\ \\ \\ \\ \\ \\ \\
5^4&=&-10x&+&4 \\
625&=&-10x&+&4 \\
-4&&&-&4 \\
\midrule
\dfrac{621}{-10}&=&\dfrac{-10x}{-10}&& \\ \\
x&=&-\dfrac{621}{10}&& \\
\end{array}\) - \(\begin{array}{rrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
9^{-2}&=&7&-&6x \\
-7&&-7&& \\
\midrule
-6x&=&-7&+&\dfrac{1}{81} \\ \\
-6x&=&-\dfrac{566}{81}&& \\ \\
x&=&\dfrac{566}{81\cdot 6}&& \\ \\
x&=&\dfrac{566}{486}&& \\ \\
x&=&\dfrac{283}{243}&&
\end{array}\) - \(\begin{array}{rrrrr}
\\ \\ \\ \\ \\ \\
2^3&=&10&-&5a \\
-10&&-10&& \\
\midrule
-5a&=&8&-&10 \\
-5a&=&-2&& \\ \\
a&=&\dfrac{2}{5}&&
\end{array}\) - \(\begin{array}{rrlrr}
\\ \\ \\
8&=&3k&-&1 \\
+1&&&+&1 \\
\midrule
9&=&3k&& \\
k&=&3&&
\end{array}\)
