https://file.aiquickdraw.com/mathbot/file/1725475458969yhpdhpop.jpg

The problem involves solving the equation by graphing a system of logarithmic equations:

\[
\log_5{5x} = \log_5{(2x + 8)}
\]

This equation simplifies to:

\[
5x = 2x + 8
\]

To solve for \( x \), subtract \( 2x \) from both sides:

\[
3x = 8
\]

Then, divide both sides by 3:

\[
x = \frac{8}{3} \approx 2.67
\]

Now, to find the approximate value of \( y \), substitute \( x \) back into either equation. Let's use the simplified form:

\[
y = \log_5(5x)
\]

Substituting \( x = 2.67 \):

\[
y \approx \log_5(5 \times 2.67)
\]

Calculating \( 5 \times 2.67 = 13.35 \), we need to calculate \( \log_5(13.35) \).

To approximate \( \log_5(13.35) \), observe that:

\[
\log_5(13.35) \approx \log_5(5^1) + \log_5(2.67)
\]

Since \( \log_5(5^1) = 1 \), and using logarithmic estimates:

\[
\log_5(13.35) \approx 1.3
\]

Thus, the point approximating the solution is around \( (2.7, 1.6) \).

This corresponds to the first choice: \( (2.7, 1.6) \).

### Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:
1. How do you convert logarithms from one base to another?
2. What is the graphical interpretation of logarithmic functions?
3. How does changing the base of a logarithm affect its graph?
4. Can you solve systems of equations involving logarithms algebraically instead of graphically?
5. What are the key properties of logarithms that simplify solving equations like this?

**Tip:** Remember that logarithmic equations can often be simplified by applying the properties of logarithms, such as the product, quotient, and power rules.

Tenisha solved the equation below by graphing a system of equations. log_5(5x) = log_5(2x + 8). Which point approximates the solution for Tenisha's system of equations?

Learn how to solve a system of logarithmic equations like log_5(5x) = log_5(2x + 8) by graphing. This problem covers key algebraic concepts and the properties of logarithms, making it suitable for students in Grades 9-12.

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