Why is a logarithm useful? And you'll see that it has very interesting properties later on. So if you want to, you can set this to be equal to an 'x', and you can restate this equation as, 3 to the 'x' power, is equal to 81. What would this evaluate to? Well this is a reminder, this evaluates to the power we have to raise 3 to, to get to 81. So with that out of the way let's try more examples of evaluating logarithmic expressions.
This is saying "hey well if I take 2 to some 'x' power I get 16'." This is saying, "what power do I need to raise 2 to, to get 16 and I'm going to set that to be equal to 'x'." And you'll say, "well you have to raise it to the fourth power and once again 'x' is equal to 4. Log, base 2, of 16 is equal to what, or is equal in this case since we have the 'x' there, is equal to 'x'? This and this are completely equivalent statements. Now the way that we would denote this with logarithm notation is we would say, log, base- actually let me make it a little bit more colourful. And this is what logarithms are fundamentally about, figuring out what power you have to raise to, to get another number. So for example, let's say that I start with 2, and I say I'm raising it to some power, what does that power have to be to get 16? Well we just figured that out.
We know that we get to 16 when we raise 2 to some power but we want to know what that power is. But what if we think about things in another way. 2 multiplied or repeatedly multiplied 4 times, and so this is going to be 2 times 2 is 4 times 2 is 8, times 2 is 16. If I were to say 2 to the fourth power, what does that mean? Well that means 2 times 2 times 2 times 2.
Condense logarithms solver how to#
So we already know how to take exponents.
Let's learn a little bit about the wonderful world of logarithms.
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