Question

Match each logarithmic expression with its equivalent value.

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(2 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
log(3)+log(6)
log(12)−log(2)
2log(3)
log(2)+log(5)
options:
:: log(6)
:: log(9)
:: log(10)
: log(18)

Answer 1

To match each logarithmic expression with its equivalent value, we will simplify each expression using the properties of logarithms (such as the product rule and quotient rule).

1. **log(3) + log(6)**
Using the product rule, this simplifies to:
\[ \log(3 \cdot 6) = \log(18) \]

2. **log(12) − log(2)**
Using the quotient rule, this simplifies to:
\[ \log\left(\frac{12}{2}\right) = \log(6) \]

3. **2log(3)**
This can be rewritten using the power rule:
\[ \log(3^2) = \log(9) \]

4. **log(2) + log(5)**
Using the product rule, this simplifies to:
\[ \log(2 \cdot 5) = \log(10) \]

Now we can match the simplified expressions:

- **log(3) + log(6)** → **log(18)**
- **log(12) − log(2)** → **log(6)**
- **2log(3)** → **log(9)**
- **log(2) + log(5)** → **log(10)**

Here are your matches:

- log(3) + log(6) = log(18)
- log(12) - log(2) = log(6)
- 2log(3) = log(9)
- log(2) + log(5) = log(10)

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