If log47≈1.404

Question

and log45≈1.161
, what is log435
? Use the rule logb(xy)=logbx+logby
to solve.(1 point)
Responses

0.827
0.827

1.630
1.630

1.209
1.209

2.565

Answer 1

To find ${\log }_{4}35$ using the given values of ${\log }_{4}7$ and ${\log }_{4}5$, we can apply the property of logarithms that states:

$${\log }_b(xy)={\log }_{b}x+{\log }_{b}y$$

Here, we can express 35 as $7\times 5$. Therefore, we can write:

$${\log }_{4}35={\log }_4(7\times 5)={\log }_{4}7+{\log }_{4}5$$

Now we substitute the approximate values provided:

$${\log }_{4}7\approx 1.404$$ $${\log }_{4}5\approx 1.161$$

Now add these two values:

$${\log }_{4}35\approx 1.404+1.161=2.565$$

Thus, the value of ${\log }_{4}35$ is approximately $2.565$.

The correct response is:

2.565