If log47≈1.404

Question

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

1.630
1.630

2.565
2.565

0.827
0.827

1.209

Answer 1

To solve for \( \log_4 35 \), we can use the property of logarithms:

\[ \log_b(xy) = \log_b x + \log_b y \]

We can express \( 35 \) as \( 7 \times 5 \). Therefore, we have:

\[ \log_4 35 = \log_4 (7 \times 5) = \log_4 7 + \log_4 5 \]

We already have \( \log_4 7 \approx 1.404 \) and \( \log_4 5 \approx 1.161 \). Now we can add these two values:

\[ \log_4 35 \approx 1.404 + 1.161 \]

Calculating this gives:

\[ \log_4 35 \approx 2.565 \]

Thus, the answer is:

2.565