Question

what is the value of \\(\log_{7} 343\\)?

\\(\bigcirc\\) \\(-3\\)

\\(\bigcirc\\) \\(-\frac{1}{3}\\)

\\(\bigcirc\\) \\(\frac{1}{3}\\)

\\(\bigcirc\\) \\(3\\)

Explanation:

⚡ Using what you learned: Evaluating Logarithmic Expressions

Step 1: Set up the equation

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

$$ \log_{7}{343} = x $$

Step 2: Rewrite in exponential form

Convert the logarithm to its exponential equivalent:

$$ 7^x = 343 $$

Step 3: Solve for \( x \)

Express \( 343 \) as a power of \( 7 \):

$$ 343 = 7^3 $$

Equating the exponents:

$$ x = 3 $$

Answer:

\( 3 \)