What value correctly evaluates log7 49^2+log7 7

Question

using the properties of logarithms?(1 point)
Responses

4
4

5
5

6
6

3

Answer 1

To evaluate \( \log_7(49^2) + \log_7(7) \) using the properties of logarithms, we can apply the following properties:

1. \( \log_b(m^n) = n \log_b(m) \)
2. \( \log_b(m) + \log_b(n) = \log_b(m \cdot n) \)

First, we can simplify \( \log_7(49^2) \):

\[ \log_7(49^2) = 2 \log_7(49) \]

Then, since \( 49 = 7^2 \):

\[ \log_7(49) = \log_7(7^2) = 2 \]

Thus,

\[ \log_7(49^2) = 2 \cdot 2 = 4 \]

Next, we find \( \log_7(7) \):

\[ \log_7(7) = 1 \]

Now we can combine these results:

\[ \log_7(49^2) + \log_7(7) = 4 + 1 = 5 \]

So, the final value is:

\[ \boxed{5} \]