Final answer:
To find log10(25) + log10(24) - log10(4), use properties of logarithms to simplify and then substitute the given values to obtain 2.186.
Step-by-step explanation:
To find the value of log10(25) + log10(24) - log10(4), we can utilize the given logarithmic values and properties of logarithms.
First, recognize that:
And because 5 is 10/2, we can use the property that the logarithm of a division of two numbers is the difference of their logarithms to express it as:
log10(10) - log10(2), which simplifies to 1 - log10(2) since the logarithm of 10 to the base 10 is 1.
Similarly, we can express log10(24) as log10(6×4), which can be split into log10(6) + log10(4). Log10(6) can be further split using log10(2×3).
Finally, we subtract log10(4), which can be represented as 2×log10(2).
Adding these up:
Thus, log10(25) + log10(24) - log10(4) is 2.186.