Question

Can you help me with my math problem. im not sure where i got it wrong

Answer 1

The value of k is;

`k=-7.1842`

Step-by-step explanation:

Given the equation:

`-3\cdot16^(-k-7)+8=3`

To solve, let us subtract 8 from both sides;

`\begin{gathered} -3\cdot16^(-k-7)+8-8=3-8 \\ -3\cdot16^(-k-7)=-5 \end{gathered}`

then, we can then divide both sides by -3;

`\begin{gathered} (-3\cdot16^(-k-7))/(-3)=(-5)/(-3) \\ 16^(-k-7)=(5)/(3) \end{gathered}`

To solve further we need to take the logarithm of both sides;

`\begin{gathered} 16^(-k-7)=(5)/(3) \\ \log 16^(-k-7)=\log (5)/(3) \\ (-k-7)\log 16=\log (5)/(3) \\ \text{dividing both sides by log 16, we have;} \\ ((-k-7)\log 16)/(\log 16)=(\log(5)/(3))/(\log16) \\ -k-7=(\log(5)/(3))/(\log16) \end{gathered}`

finding the value of the log;

`-k-7=0.1842\text{ (to 4 decimal place)}`

solving for k;

`\begin{gathered} -k-7=0.1842 \\ -k=0.1842+7 \\ -k=7.1842 \\ k=-7.1842 \end{gathered}`

Therefore, the value of k is;

`k=-7.1842`