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]
