Answered

Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Drag the tiles to the correct boxes to complete the pairs.

Match each equation with its solution.

[tex]\[
\begin{array}{c}
\ln (x+5)=\ln (x-1)+\ln (x+1) \\
\log _4\left(5 x^2+2\right)=\log _4(x+8) \\
e^{x^2}=e^{4 x+5} \\
\log (x-1)+\log 5 x=2 \\
\end{array}
\][/tex]

[tex]\[
\begin{array}{c}
(-1, \frac{6}{5}) \longrightarrow \square \\
\text{only } 5 \rightarrow \square \\
\text{only } 3 \rightarrow \square \\
(-1, 5) \longrightarrow \square \\
\end{array}
\][/tex]

Sagot :

GinnyAnswer
Sure! Let's match each equation with its solution.

1. Given the equation [tex]\(\ln(x+5) = \ln(x-1) + \ln(x+1)\)[/tex], the solution is [tex]\( x = 3 \)[/tex].

2. Given the equation [tex]\(\log_4(5x^2+2) = \log_4(x+8)\)[/tex], the solutions are [tex]\( x = 1.2 \)[/tex] and [tex]\( x = -1.0 \)[/tex].

3. Given the equation [tex]\(e^{x^2} = e^{4x+5}\)[/tex], the solutions are [tex]\( x = 5.0 \)[/tex] and [tex]\( x = -1.0 \)[/tex].

4. Given the equation [tex]\(\log(x-1) + \log(5x) = 2\)[/tex], the solutions are [tex]\( x = 5.0 \)[/tex] and [tex]\( x = -4.0 \)[/tex].

Here are the matches:

- [tex]\(\ln(x+5) = \ln(x-1) + \ln(x+1)\)[/tex] only [tex]\(\rightarrow\)[/tex] only 3
- [tex]\(\log_4(5x^2+2) = \log_4(x+8)\)[/tex] [tex]\(\rightarrow\)[/tex] [tex]\((-1, 1.2)\)[/tex]
- [tex]\(e^{x^2} = e^{4x+5}\)[/tex] [tex]\(\rightarrow\)[/tex] [tex]\((-1, 5.0)\)[/tex]
- [tex]\(\log(x-1) + \log(5x) = 2\)[/tex] [tex]\(\rightarrow\)[/tex] [tex]\(5\)[/tex]

Hence:

- [tex]\(\ln(x+5) = \ln(x-1) + \ln(x+1)\)[/tex] [tex]\(\rightarrow\)[/tex] only 3
- [tex]\(\log_4(5x^2+2) = \log_4(x+8)\)[/tex] [tex]\(\rightarrow\)[/tex] [tex]\((-1, 1.2)\)[/tex]
- [tex]\(e^{x^2} = e^{4x+5}\)[/tex] [tex]\(\rightarrow\)[/tex] [tex]\((-1, 5.0)\)[/tex]
- [tex]\(\log(x-1) + \log(5x) = 2\)[/tex] [tex]\(\rightarrow\)[/tex] 5
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.