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40 votes
If log10(2)= 0.301 and log10(3)= 0.417;
find log10(25) + log10(24) - log10(4)​

User Juraj Petrik
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2 Answers

11 votes
11 votes

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.

User Deroccha
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17 votes
17 votes
Log10(25)+log10(24) - log10(4)= 45!
User Mehran Hatami
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