Use a calculator to find approximations of the common logarithms.

(a) [tex]$\log (758.4)$[/tex]

(b) [tex]$\log (75.84)$[/tex]

(c) [tex]$\log (7.584)$[/tex]

(a) [tex]$\log (758.4) \approx$[/tex] [tex]$\square$[/tex]

(Simplify your answer. Round to four decimal places as needed.)



Answer :

To find the approximations of the common logarithms, we will proceed step-by-step for each given value. The common logarithm [tex]\(\log(x)\)[/tex] is the logarithm to the base 10.

### (a) [tex]\(\log(758.4)\)[/tex]
First, we need to calculate the common logarithm of [tex]\(758.4\)[/tex].

[tex]\[ \log(758.4) \approx 2.8799 \][/tex]

So, the approximate value for [tex]\(\log(758.4)\)[/tex] rounded to four decimal places is:

[tex]\[ \boxed{2.8799} \][/tex]

### (b) [tex]\(\log(75.84)\)[/tex]
Next, we calculate the common logarithm of [tex]\(75.84\)[/tex].

[tex]\[ \log(75.84) \approx 1.8799 \][/tex]

So, the approximate value for [tex]\(\log(75.84)\)[/tex] rounded to four decimal places is:

[tex]\[ \boxed{1.8799} \][/tex]

### (c) [tex]\(\log(7.584)\)[/tex]
Finally, we calculate the common logarithm of [tex]\(7.584\)[/tex].

[tex]\[ \log(7.584) \approx 0.8799 \][/tex]

So, the approximate value for [tex]\(\log(7.584)\)[/tex] rounded to four decimal places is:

[tex]\[ \boxed{0.8799} \][/tex]

To summarize:
- [tex]\(\log(758.4) \approx 2.8799\)[/tex]
- [tex]\(\log(75.84) \approx 1.8799\)[/tex]
- [tex]\(\log(7.584) \approx 0.8799\)[/tex]