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

1 answer

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