Solve the equation. Write the solution set with the exact solutions.

If there is more than one solution, separate the answers with commas.
There is no solution, .
The exact solution set is

Ask by Weston French. in the United States

Mar 25,2025

Question

Solve the equation. Write the solution set with the exact solutions.

If there is more than one solution, separate the answers with commas.
There is no solution, .
The exact solution set is

Ask by Weston French. in the United States

Mar 25,2025

UpStudy AI · Accepted Answer

Solve the equation $$ \log(w^{2}+7w)=\log(8) $$.
Solve the equation by following steps:
- step0: Solve for $$w$$:
  $$\log_{10}{\left(w^{2}+7wight)}=\log_{10}{\left(8ight)}$$
- step1: Find the domain:
  $$\log_{10}{\left(w^{2}+7wight)}=\log_{10}{\left(8ight)},w \in \left(-\infty,-7ight)\cup \left(0,+\inftyight)$$
- step2: Simplify:
  $$w^{2}+7w=8$$
- step3: Move the expression to the left side:
  $$w^{2}+7w-8=0$$
- step4: Factor the expression:
  $$\left(w-1ight)\left(w+8ight)=0$$
- step5: Separate into possible cases:
  $$\begin{align}&w-1=0\&w+8=0\end{align}$$
- step6: Solve the equation:
  $$\begin{align}&w=1\&w=-8\end{align}$$
- step7: Check if the solution is in the defined range:
  $$\begin{align}&w=1\&w=-8\end{align},w \in \left(-\infty,-7ight)\cup \left(0,+\inftyight)$$
- step8: Find the intersection:
  $$\begin{align}&w=1\&w=-8\end{align}$$
- step9: Rewrite:
  $$w_{1}=-8,w_{2}=1$$
The solution set to the equation $$ \log \left(w^{2}+7wight)=\log 8 $$ is $$ w=-8, w=1 $$.
The exact solution set is $$ w = -8, 1 $$.

Solve the equation. Write the solution set with the exact solutions.

If there is more than one solution, separate the answers with commas.
There is no solution, .
The exact solution set is

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Solve the equation. Write the solution set with the exact solutions. If there is more than one solution, separate the answers with commas. There is no solution, . The exact solution set is

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Solve the equation. Write the solution set with the exact solutions.

If there is more than one solution, separate the answers with commas.
There is no solution, .
The exact solution set is