https://file.aiquickdraw.com/mathbot/file/1729306424585v3n5m43y.jpg

The problem in the image is asking to evaluate:

\[
\log_6(1)
\]

In general, for any logarithm \(\log_b(x)\), it asks "to what power must the base \(b\) be raised to give \(x\)?"

In this case:

\[
\log_6(1) = ?
\]

This expression is asking "to what power must 6 be raised to give 1?"

The answer is \(0\), because any non-zero number raised to the power of 0 equals 1:

\[
6^0 = 1
\]

Therefore:

\[
\log_6(1) = 0
\]

Would you like more details on logarithmic properties or any related topics? Here are 5 related questions to explore:

1. How do you evaluate logarithms with different bases?
2. What are the properties of logarithms that can simplify expressions?
3. How do logarithms relate to exponential functions?
4. What is the change of base formula for logarithms?
5. How can logarithms be applied in solving real-world problems?

**Tip:** Always remember that \(\log_b(1)\) is 0 for any base \(b > 0\).

Learn how to evaluate the logarithmic expression log base 6 of 1. This problem demonstrates key logarithmic concepts and uses the identity log_b(1) = 0 for any base b. Suitable for high school students in Grades 9-12.

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