Question

I need help on this practice problem It asks to solve the logarithmic equations. Number 3. And 4.

Answer 1

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}`