Question

complete the steps to evaluate the following expression, given \\(\log_{3}a = -0.631\\).

\\\log_{3}\frac{a}{3}\\

\\(\log_{3}3 = \\)

Explanation:

⚡ Using what you learned: properties of logarithms

Step 1: Evaluate the basic logarithm

Evaluate the expression in the box:

$$ \log_{3}3 = 1 $$

Step 2: Apply the quotient property

Expand the given expression \( \log_{3}\frac{a}{3} \) using the quotient rule:

$$ \log_{3}\frac{a}{3} = \log_{3}a - \log_{3}3 $$

Step 3: Substitute and calculate

Substitute the given values \( \log_{3}a = -0.631 \) and \( \log_{3}3 = 1 \):

$$ -0.631 - 1 = -1.631 $$

Answer:

The value for the box is:

$$ \log_{3}3 = 1 $$

The fully evaluated expression is:

$$ -1.631 $$