Logarithms are yet another operation. they might seem difficult but when you look at them very closely, you can see that they is actually a very simple topic. Logarithms are kind-of like another operation, but when you actually know what it is, it is nothing more than an exponent "placeholder".
ISAIAH LOPEZ
Ok, so before I start giving examples of logarithms, I need to tell you what they actually are. A logarithm can be defined as the exponent that 10 would need to be raised to to equal x. For example if you calculate the log of 100, it would be 2 because 10² = 100. Log(100) = 2. See it? if you asked what log(1,000) would be, the answer is 3 because 10 would have to be raised to the third power to equal 1,000. You could even take log(10,000,000), which is 7 because 10 to the seventh power gives you 10,000,000.
There are probably three questions you are asking right now. The first is, if logarithms go by the base of ten, then what is the log(10)? Well, the logarithm of 10 would be 1 actually because 10¹=10. Another cool question you are probably asking is what is log(1)? This might seem like a tricky one, but actually it is not. Remember that anything to the zero power is equal to 1 so 10 raised to the zero power is one, and therefore the log(1) is 0. The last question you are probably asking is, what if you "log" a number less than 1, or a fraction? Well remember than a negative exponent results in that of it's positive counterpart, with the exception that there's a one over it. So log(1/10) = -1, and log(10,000) = -4. One more thing to keep in mind is that the logarithm of zero is undefined, because 10 can't be raised to any power to equal zero.
The logarithms of numbers doesn't just have to be tens exponent multiples. I have just done that in this lesson to simplify everything. You can even take the log of something that isn't an exponent of 10, like log(2), but it would just be hard because all the other numbers would end up in a weird decimal.