1 Answer

Tyleha · Answer 1 · 2023-09-08T19:08:51+0000

3) You have the following expression:

$\log _p4096=3$

In order to solve for p, proceed as follow:

- Use the property:

$\log _mn=(\log n)/(\log m)$

which applied to the given expression result:

$(\log 4096)/(\log p)=3$

- Next, solve for log p and take the complete equation as the exponent of a base 10:

$\begin{gathered} \log p=(1)/(3)\log 4096 \\ 10^(\log p)=10^{(1)/(3)\log 4096} \end{gathered}$

- By properties of logarithms you obtain:

$\begin{gathered} p=4096^{(1)/(3)}=\sqrt[3]{4096^{}} \\ p=16 \end{gathered}$

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