Question

If log4≈0.6021
log
⁡
4
≈
0.6021
and log18≈1.2553
log
⁡
18
≈
1.2553
, which of the following is the value of log72
log
⁡
72
?(1 point)
Responses

log72≈2.0849
log
⁡
72
≈
2.0849
logarithm 72 approximately equals 2.0849

log72≈0.6532
log
⁡
72
≈
0.6532
logarithm 72 approximately equals 0.6532

log72≈1.8574
log
⁡
72
≈
1.8574
logarithm 72 approximately equals 1.8574

log72≈0.7558

Answer 1

To find \( \log_{10} 72 \), we can use the properties of logarithms, specifically the multiplication rule:

\[
\log(ab) = \log a + \log b
\]

First, we can express 72 in terms of numbers for which we already have logarithm values. Notice that:

\[
72 = 8 \times 9 = 2^3 \times 3^2
\]

We can also break this down into:

\[
72 = 18 \times 4
\]

Now we can use the logarithm values provided:

1. \( \log 18 \approx 1.2553 \)
2. \( \log 4 \approx 0.6021 \)

Using the multiplication rule:

\[
\log 72 = \log(18 \times 4) = \log 18 + \log 4
\]

Now substituting the values:

\[
\log 72 \approx 1.2553 + 0.6021 \approx 1.8574
\]

Thus, the value of \( \log_{10} 72 \) is approximately:

\[
\log 72 \approx 1.8574
\]

So the correct answer is:

**log72≈1.8574**