Find each value. If applicable, give an approximation to four dec...

Question

Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 518/342

Accepted Answer

Hello everybody. I'm doing all right. Today. Today we're gonna be looking at this math question that's asking us to evaluate the following logarithmic expression. And if it is appropriate to write the answer in decimal round it to four decimal places, now, the expression that they give us is log of 652 divided by 264. And the answer choice that they provide us are a four B 0.3926 C 1.725 and the 2.7273. Now, when looking at a question like this, I see that we have a log of a division. Now, the first thing that I can think of to simplify this is, is there any way to simplify the actual division itself? So we're looking at it as a fraction, do the numerator and the denominator have a common factor that we can divide each of them by and simplify. In this case, they do. And that factor will be four. So we can divide both the narrator and the denominator by four. And let's just rewrite that. So we'll have log of divided by four, over divided by four. And that will give a log of divided by 66. So now we simplified the equation that we originally had into some smaller numbers. Now we have a log of a fraction or a division and we can do a simple recall of some rules that we have about logs to see how we can rewrite this to something else. So in this case, I'm gonna, I'm gonna write a general rule for the quo rule. So let's say we have log of base B of A divided by C, that would be equal to log of base B of A minus log of base B of C. So when comparing that to the equation that we have, now we see that we have a log and no specified base when this happens and they just, they just write log with no specified base. That base will be 10. We can assume that base is 10. So that 10 will be the B in our recall equation, the 163 or the numerator will be the A in our recall and the 66 or the denominator will be the C in our recall. So using that information, let's rewrite what we have. So we'll have log of 100 and minus log of 66. And now there's nothing else we can do to simplify this further. So basically what we had originally, uh the log of 100 and 63 divided by 66 is the same as log of 100 and 63 minus log of 66. So if we, anything we can do now is just switch back to the division back and forth. So we can't go any further. So you can plug either of those equations into your calculator, whether you prefer log of 100 and 63 divided by 66 or subtracting log of 100 and 63 minus log of 66. You can plug either of those into your calculator and I'll write the calculator answer here and that answer will be 0. four and so on. Now, they asked us for four decimal places. So we stop it at the six and we see that the number after the six is a four. So we don't have to round up. So our answer will remain at 0. or in this case, letter B. So I hope that was helpful. And until next time.

Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 518/342

Key Concepts

Logarithms

Change of Base Formula

Approximation and Rounding

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