This section, we want to use our calculators to find some values of some common logarithms and also some natural logarithms (ln log).
So, here's our first problem. Let's find on the calculator log378. Now you know, when the base isn't showing—when it says log378—
we're assuming that the base is 10. So, on your calculator, you want to look for that button that says "LOG"; that'll be your logarithm button;
and if you press that button on your calculator after you've entered 378 or before, depending on the kind of calculator you have,
you can check to see: this will come out 2.5775. And I round it up to this place right here, just so I can write something down here.
Your calculator will show more digits than this, but all you want to do is to be able to use your calculator to look up log₁₀378.
It's just a matter of pressing that logarithm button. Let's look at the next problem here: 0.378. I want to find the common log of that, log₁₀.
Do that on the calculator. You can try it along with me. Your calculator should say -0.4225.
And again, I rounded that last place right there. So, log₁₀0.378—it's just a matter of using that logarithm button, log₁₀ button
on your calculator to get this. Let's look at some ln logs. ln log378; you know that when you see this notation,
it's a logarithm with an implied base of e<—that naturally occurring constant e. So, if I do this on the calculator, press 378,
and then look for the button on your calculator that says "LN" for natural logarithm. You should get 5.9349. And again, I rounded that one up.
So ln log, logₑ on the calculator—you have to look for your ln log button;
378 with that button should give you 5.9349. Here's another one: ln log e. Well, remember that the base here is e
when I see this notation, so I don't even have to use the calculator. What number do I raise e to in order to get e? And the answer is 1.
Of course, on your calculator, if you would have pressed the button labeled "e" and then after that pressed your ln log button,
you should have ended up with 1 on your calculator, also. So, that's a look at how we find some common logarithms
and ln logarithms using the calculator. Let's go in the other direction now, and give them the logarithm,
and see if we can find the number it came from. First problem: log₁₀x = 2.8802.
So again, this is notation that implies that the base is 10. We know from our definition of logarithms that this means
that 10 to this number must be equal to x. So, this is the same as saying 10^2.8802 = x.
So, I need to look on my calculator for the button that had "10ˣ"; it's usually right around where my ln logarithm button is;
sometimes it's the inverse of that button; and when I use that button with this number 2.8802, I should end up with x =,
and let's see what I got: I round off—759. So, try that "10ˣ" button on your calculator, the inverse of your log button;
and when you press that, you should get rounded at three decimal places 759 when you look up 10^2.8802. Here's another one: log x = 1.8802.
Again on my calculator, I look for the button labeled "10ˣ," press that button with the number 1.8802, and it should be x = 75.9
and that's what it is rounded off; your calculator will show a few more digits than this, but when you round it off, you should get 75.9.
Okay, so this is just how to find this number on a calculator; we're saying, the log₁₀ is this—that means that x itself must be 75.9.
If you want to check this, you can enter this into the calculator, press your logarithm button, and see if you don't get 1.8802.
One more problem: ln log x or, yeah, ln log x = 2.8802. Remember this is e, so I'm looking for my "eˣ" button;
I want to use my "eˣ" button with this number right here. When I do that, x = 17.8.
So, if the ln log x = 2.8802, then x itself must be 17.8.
So, you want to check this on your calculator, using your "eˣ" button, and see if you can't get that 17.8 yourself.