What value correctly evaluates log7492+log77

Question

log
7
⁡
49
2
+
log
7
⁡
7
using the properties of logarithms?(1 point)
Responses

5
5

4
4

3
3

6

Answer 1

To evaluate \( \log_7{49} + \log_7{7} \) using the properties of logarithms, we can use the property that states:

\[ \log_b{m} + \log_b{n} = \log_b{(m \cdot n)} \]

In this case, we have: \[ \log_7{49} + \log_7{7} = \log_7{(49 \cdot 7)} \]

Now, calculate \( 49 \cdot 7 \): \[ 49 \cdot 7 = 343 \]

Next, we can simplify this expression: \[ \log_7{343} \]

Since \( 343 = 7^3 \), we can write: \[ \log_7{343} = \log_7{(7^3)} = 3 \]

Thus, the value of \( \log_7{49} + \log_7{7} \) is \( 3 \).

The correct answer is: \[ 3 \]