Question

If log28≈1.4472
log
⁡
28
≈
1.4472
and log5≈0.6990
log
⁡
5
≈
0.6990
, which of the following is the value of log140
log
⁡
140
?(1 point)
Responses

log140≈2.1462
log
⁡
140
≈
2.1462
logarithm 140 approximately equals 2.1462

log140≈7.2360
log
⁡
140
≈
7.2360
logarithm 140 approximately equals 7.2360

log140≈0.7482
log
⁡
140
≈
0.7482
logarithm 140 approximately equals 0.7482

log140≈1.0116

Answer 1

To calculate \( \log 140 \), we can use the properties of logarithms. We can express 140 in terms of its prime factors:

\[
140 = 28 \times 5
\]

Using the logarithmic property \( \log(ab) = \log a + \log b \), we can write:

\[
\log 140 = \log(28 \times 5) = \log 28 + \log 5
\]

Now, substituting the approximate values given:

\[
\log 28 \approx 1.4472
\]
\[
\log 5 \approx 0.6990
\]

So we have:

\[
\log 140 \approx 1.4472 + 0.6990
\]

Calculating this gives:

\[
\log 140 \approx 2.1462
\]

Thus, the value of \( \log 140 \) is approximately \( 2.1462 \).

The correct response is:

**log140≈2.1462**