How do logarithms convert numbers like 8.7 and -2.3 to whole numbers?

[mohabitar]

I am unsure of how they were able to change 8.7 to 8 and make -2.3 to 2. Whats the explanation behind this?

 

[CRGreathouse]

I am unsure of how they were able to change 8.7 to 8 and make -2.3 to 2. Whats the explanation behind this?

It's not that 8.7 was changed to 8, but that $$\lfloor8.7\rfloor$$ was changed to 8,since 8.7 rounded down is 8.

 

[Mark44]

And $$\lceil -2.3 \rceil$$ is rounded up to -2.

 

[mohabitar]

Ohhhh I didnt even notice those were the ceiling and floor functions, I thought they were just brackets! Thanks!

 

[CellCoree]

The explanation behind this is that logarithms are a mathematical operation that involves finding the power to which a base number must be raised to equal a given number. In this case, the base number is 10 and the given number is 8.7. The logarithm of 8.7 is approximately 0.939519, which can be rounded to 0.9. Similarly, the logarithm of -2.3 is approximately -0.361728, which can be rounded to -0.3. This is how 8.7 was changed to 8 and -2.3 was changed to 2. It is important to note that logarithms can only be taken of positive numbers, so the negative sign in front of -2.3 is dropped when calculating the logarithm. I hope this explanation helps clarify the process of converting these numbers using logarithms.