Question

Solve the logarithmic equation. Write the answer in exact, simplified form.log (-p) + log 6 = log (7p-26)The solution set is.()

Answer 1

We have to solve the logarithmic equation:

$\log (-p)+\log 6=\log (7p-26)$

We can start by applying the product rule to the terms in the left side:

$\begin{gathered} \log (-p)+\log 6=\log (7p-26) \\ \log (-p\cdot6)=\log (7p-26) \end{gathered}$

Then, as both sides apply the same logarithm and are the only terms, the arguments of both have to be equal:

$\begin{gathered} -p\cdot6=7p-26 \\ -6p=7p-26 \\ -6p-7p=-26 \\ -13p=-26 \\ p=\frac{-26}{-13} \\ p=2 \end{gathered}$

Answer: p = 2