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: $$3$$