To solve for the body fat percentage using the given formula:
[tex]\[
\% \text{ Grasa corporal} = 1.0324 - 0.19077 \times \log(\text{cintura} - \text{cuello}) + 0.15456 \times \log(\text{altura}) - 450
\][/tex]
we'll break down the calculation step-by-step with the provided measurements:
1. Given Measurements:
- Cintura (waist): 82 cm
- Cuello (neck): 38 cm
- Altura (height): 175 cm
2. Calculating [tex]\(\log(\text{cintura} - \text{cuello})\)[/tex]:
[tex]\[
\text{cintura} - \text{cuello} = 82 - 38 = 44
\][/tex]
[tex]\[
\log(44) \approx 3.784
\][/tex]
3. Calculating [tex]\(\log(\text{altura})\)[/tex]:
[tex]\[
\log(175) \approx 5.165
\][/tex]
4. Substituting these values into the formula:
[tex]\[
\% \text{ Grasa corporal} = 1.0324 - 0.19077 \times 3.784 + 0.15456 \times 5.165 - 450
\][/tex]
5. Breaking down the multiplication:
- [tex]\(0.19077 \times 3.784 \approx 0.7213 \)[/tex]
- [tex]\(0.15456 \times 5.165 \approx 0.7990 \)[/tex]
6. Putting it all together:
[tex]\[
\% \text{ Grasa corporal} = 1.0324 - 0.7213 + 0.7990 - 450
\][/tex]
7. Simplifying the expression:
[tex]\[
\% \text{ Grasa corporal} \approx 1.0324 + 0.7990 - 0.7213 - 450
\][/tex]
[tex]\[
\approx 1.8314 - 0.7213 - 450
\][/tex]
[tex]\[
\approx 1.1101 - 450
\][/tex]
[tex]\[
\approx -448.89
\][/tex]
So, the body fat percentage according to the given formula and the specified measurements is approximately [tex]\(-448.89\%\)[/tex].
