Question

which equation can you use to evaluate \\(\log_{6} 1,296\\)?

\\(a^{6} = 1,296\\)

\\(6^{a} = 1,296\\)

\\(6a = 1,296\\)

evaluate: \\(\log_{6} 1,296 = \\)

Explanation:

⚡ Using what you learned: Understanding Logarithmic Functions

Step 1: Convert to exponential form

Set the logarithmic expression equal to a variable \( x \):

$$ \log_{6}(1,296) = x $$

Using the definition of a logarithm, rewrite it in exponential form:

$$ 6^x = 1,296 $$

Step 2: Solve for x

Find the power of \( 6 \) that equals \( 1,296 \):

$$ 6^1 = 6 $$

$$ 6^2 = 36 $$

$$ 6^3 = 216 $$

$$ 6^4 = 1,296 $$

Thus, \( x = 4 \).

Answer:

• Equation to use: \( 6^x = 1,296 \)
• Evaluated value: \( \log_{6}(1,296) = 4 \)