Question

Write full solution.Find the domain and solve the following equation:log,(x-5)+log, (x+3) = 1

Answer 1

We have the following equation:

$\log _,(x-5)+\log _,(x+3)=1$

First, we apply the apply the following rule:

$\begin{gathered} \log _ab+\log _ac=\log _ab\cdot c \\ \log _,(x-5)+\log _,(x+3)=\log _,(x-5)\cdot(x+3) \\ \log _,(x-5)\cdot(x+3)=1 \\ \end{gathered}$

For any non null number, we have:

$n^0=1$

Therefore, we have:

$\begin{gathered} (x-5)\cdot(x+3)=0 \\ x_1=5 \\ x_2=-3 \end{gathered}$