What value correctly evaluates

Question

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

6
6

3
3

4
4

5

Answer 1

To evaluate the expression \( \log_7 49 + \log_7 7 \), we can use the properties of logarithms.

1. First, evaluate \( \log_7 49 \): \[ 49 = 7^2 \quad \Rightarrow \quad \log_7 49 = \log_7(7^2) = 2 \]

2. Next, evaluate \( \log_7 7 \): \[ \log_7 7 = 1 \]

3. Now add the two results together: \[ \log_7 49 + \log_7 7 = 2 + 1 = 3 \]

Thus, the correct value that evaluates \( \log_7 49 + \log_7 7 \) is \( \boxed{3} \).