Evaluate the expression without using a calculator.

log Subscript 3 Baseline 3 Superscript 8

To evaluate the expression \( \log_3 3^8 \), we can apply the logarithmic property:

\[
\log_b (b^x) = x
\]

In this case, \( b = 3 \) and \( x = 8 \). Therefore,

\[
\log_3 3^8 = 8
\]

Thus, the value of the expression is \( 8 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is \( \log_2 2^5 \)?
2. How do you simplify \( \log_4 4^6 \)?
3. What is \( \log_{10} 10^3 \)?
4. Can you explain the general formula for \( \log_b (b^x) \)?
5. What is the value of \( \log_5 5^9 \)?

**Tip**: Always remember that \( \log_b (b^x) = x \), which simplifies logarithmic expressions involving powers of the base.

Evaluate the expression without using a calculator: log Subscript 3 Baseline 3 Superscript 8

This detailed guide explains how to evaluate the logarithmic expression log_3 3^8 using key logarithmic properties and the identity log_b (b^x) = x. Suitable for high school students in Grades 9-12.

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