Answer:
The value of k is;
[tex]k=-7.1842[/tex]
Explanation:
Given the equation:
[tex]-3\cdot16^{-k-7}+8=3[/tex]
To solve, let us subtract 8 from both sides;
[tex]\begin{gathered} -3\cdot16^{-k-7}+8-8=3-8 \\ -3\cdot16^{-k-7}=-5 \end{gathered}[/tex]
then, we can then divide both sides by -3;
[tex]\begin{gathered} \frac{-3\cdot16^{-k-7}}{-3}=\frac{-5}{-3} \\ 16^{-k-7}=\frac{5}{3} \end{gathered}[/tex]
To solve further we need to take the logarithm of both sides;
[tex]\begin{gathered} 16^{-k-7}=\frac{5}{3} \\ \log 16^{-k-7}=\log \frac{5}{3} \\ (-k-7)\log 16=\log \frac{5}{3} \\ \text{dividing both sides by log 16, we have;} \\ \frac{(-k-7)\log 16}{\log 16}=\frac{\log\frac{5}{3}}{\log16} \\ -k-7=\frac{\log\frac{5}{3}}{\log16} \end{gathered}[/tex]
finding the value of the log;
[tex]-k-7=0.1842\text{ (to 4 decimal place)}[/tex]
solving for k;
[tex]\begin{gathered} -k-7=0.1842 \\ -k=0.1842+7 \\ -k=7.1842 \\ k=-7.1842 \end{gathered}[/tex]
Therefore, the value of k is;
[tex]k=-7.1842[/tex]
