Question

I need help on this I need it answered, Step by step

Answer 1

The following exponential, and logarithmic forms are equivalent

`\begin{gathered} \log _b(a)=x\Longleftrightarrow b^x=a \\ \text{where} \\ b\text{ is the base} \end{gathered}`
`\begin{gathered} \text{Given that} \\ \log _p(4096)=3 \\ \\ \text{We can convert this into the exponential form} \\ \log _p(4096)=3\Longrightarrow p^3=4096 \end{gathered}`

We can now solve p by getting the cube root of both sides

`\begin{gathered} p^3=4096 \\ \sqrt[3]{p^3}=\sqrt[3]{4096} \\ p=16 \end{gathered}`

Therefore, the base of the logarithm is 16.