Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions.

(Simplify your answer.)

Ask by Stewart Mills. in the United States

Mar 21,2025

Question

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions.

(Simplify your answer.)

Ask by Stewart Mills. in the United States

Mar 21,2025

UpStudy AI · Accepted Answer

We start with the expression:
$$
\log 125 + \log 8
$$

**Step 1. Apply the Product Rule**

The product rule for logarithms states that:
$$
\log a + \log b = \log (ab)
$$
Thus,
$$
\log 125 + \log 8 = \log (125 \times 8)
$$

**Step 2. Multiply the Arguments**

Calculate:
$$
125 \times 8 = 1000
$$
So, the expression becomes:
$$
\log (125 \times 8) = \log 1000
$$

**Step 3. Evaluate the Logarithm (if possible)**

If the logarithm is assumed to be base $$10$$, then:
$$
\log 1000 = 3 \quad \text{since} \quad 10^3 = 1000.
$$

Thus, the final condensed expression is:
$$
\log 125 + \log 8 = \log 1000 = 3
$$
$$ \log 125 + \log 8 = \log 1000 = 3 $$