To estimate the value of [tex]$\log_{10} 6.25$[/tex], we need to understand that logarithm base 10 (common logarithm) helps us find the power to which 10 must be raised to obtain the given number.
Here's a step-by-step outline to estimate [tex]$\log_{10} 6.25$[/tex]:
1. Identify the number for which we need to find the logarithm. In this case, it's 6.25.
2. Use the value provided for [tex]$\log_{10} 6.25$[/tex] which is approximately 0.7958800173440752.
3. Compare this value with the given options to see which one closely matches:
- A. 7482
- B. 8092
- C. 7853
- D. 7959
When matching the digits of the provided number (0.7958800173440752) with the given options, we see that:
- The digits 7482 do not align with the given result.
- The digits 8092 do not align with the given result.
- The digits 7853 do not align with the given result.
- The digits 7959 closely match 0.7958800173440752 (up to three decimals: 0.795).
Thus, the correct approximation from the options provided would be:
D. 7959
