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 0.0022

Accepted Answer

Hello everybody. I hope you're doing 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 0.77. And the answers of the providers are a negative 2.1135 B negative 1.8701 C negative 2.5887 and D 77. Now, when I look at the expression that we have and I see the number 0.77, I can think of a different way to write this as a fraction form and that'll be of 77 divided by 10,000. So with that information, I can rewrite the expression that we have as a log of divided by 10,000. And that is the same as what we had originally just as a fraction form and as a fraction that, that's also dividing. I can think of the quotient rule that algorithms have to rewrite this differently. So I can recall the caution room and write a general formula for it that we can compare with our expression. So let's just say that you have log of base B of A divided by C that's equal to log of base B of A minus log of base B of C. So comparing that to the expression that we have, we see that we have a log with no specified base when this is the case, that means that the base is 10. So that 10 will be the B in our recall, the numerator or the 77 will be the A in a recall. And the denominator or the 10,000 will be the C in our recall. So using that information, let's rewrite the expression that we have and that will give us a log of 77 minus log up 10,000. Now, once we reach this point, there is no other way to rewrite this. So the quotient rule works forwards and backwards. So you can theoretically go back to the fraction form, but that won't get you anywhere. So you can have the, the subtraction form that we have now a blog of 77 minus log of 10, or you can use the quo rule to go back to the fraction that we had at log or divided by 10,000. They will both be the same. Now, we're because of that, we're left with just plugging this into our calculator to see what answer is provided. And just so, you know, you can know, you can plug any of the three expressions in into your calculator and they'll give you the same answer. So you can plug in log of 0.77, log of 77 divided by 10,000 or log of 77 minus log of 10,000. And they will all be the same answer. So once you plug that into your calculator, the calculator answer will be without rounding will be negative 2.11 350 and so on. And now they asked us to round to four decimal places. So we stop it at the five and the number that comes after the five is a zero. So we don't have to round up. Therefore, we're left with a final answer of negative 2. 35. And that'll be the answer for this question or in this case letter A. So I hope that was helpful. And until next time.

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Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 0.0022