If log47≈1.404

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

1 answer

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