https://file.aiquickdraw.com/mathbot/file/1725844059123p8m1v09p.jpg

To solve the equation provided in the image, which is:

\[ \log_6 64 - \log_6 125 \]

We can use the logarithmic property that states:

\[ \log_b a - \log_b c = \log_b \left(\frac{a}{c}\right) \]

Applying this property here, we get:

\[ \log_6 \left(\frac{64}{125}\right) \]

Now, this expression represents the power to which 6 must be raised to yield the fraction \(\frac{64}{125}\). Let's calculate this logarithmic value:

\[ \log_6 \left(\frac{64}{125}\right) = \frac{\log \left(\frac{64}{125}\right)}{\log 6} \]

Let's calculate this value to get the solution.The solution to the equation \(\log_6 64 - \log_6 125\) is approximately \(-0.374\).

Would you like more details on this solution or have any other questions?

Here are five related questions you might consider:
1. How would the solution change if the base of the logarithms were different?
2. What are the properties of logarithms that were used to solve this problem?
3. How does the solution change if the numbers 64 and 125 are swapped?
4. Can you explain how logarithms are used in real-life applications?
5. What are some other examples of equations involving logarithms that can be solved using properties?

**Tip:** Always remember to simplify the terms inside the logarithm as much as possible before evaluating, to make calculations easier and more straightforward.

Learn how to solve the logarithmic expression log_6 64 - log_6 125 using logarithmic properties and the change of base formula. This problem demonstrates key concepts in logarithms, algebra, and is suitable for students in Grades 9-12.

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