https://file.aiquickdraw.com/mathbot/file/1723597477645x7mk8m3e.jpg

The equation in the image is:

\[
\log_3{72} + \log_3{3} - \log_3{7}
\]

Let's solve this step by step:

### Step 1: Apply the logarithm properties

1. **Sum of logarithms**: \(\log_a{b} + \log_a{c} = \log_a{(b \times c)}\)
2. **Difference of logarithms**: \(\log_a{b} - \log_a{c} = \log_a{\left(\frac{b}{c}\right)}\)

So, we can rewrite the expression:

\[
\log_3{72} + \log_3{3} - \log_3{7} = \log_3{\left(72 \times 3\right)} - \log_3{7}
\]

\[
= \log_3{\left(\frac{72 \times 3}{7}\right)}
\]

### Step 2: Simplify the expression inside the logarithm

Calculate the value inside the logarithm:

\[
72 \times 3 = 216
\]

Now, divide by 7:

\[
\frac{216}{7} \approx 30.857
\]

Thus, the expression simplifies to:

\[
\log_3{30.857}
\]

### Step 3: Final Answer

The final expression is:

\[
\log_3{30.857}
\]

This is the exact expression, but if you want to approximate the numerical value:

\[
\log_3{30.857} \approx 3.091
\]

Would you like more details or have any further questions?

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Here are 8 related questions:

1. How do you solve logarithmic equations with different bases?
2. What is the change of base formula for logarithms?
3. Can logarithms of negative numbers be evaluated?
4. What are the main properties of logarithms?
5. How can logarithms be used to solve exponential equations?
6. What is the natural logarithm and how does it differ from common logarithms?
7. How do you graph a logarithmic function?
8. How does the logarithm function relate to exponential decay?

**Tip:** When working with logarithms, always try to simplify the expression using logarithm properties before evaluating the final result.

Learn how to solve the logarithmic equation log3(72) + log3(3) - log3(7) step-by-step with detailed explanations. This problem involves logarithm properties such as sum and difference of logarithms, suitable for high school students.

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