If log4≈0.6021

Question

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