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(387 * 23)

Accepted Answer

Hello everybody, everything. 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 261 multiplied by 17. And the answer choices that they provide us are a 3.1092 B 2.8352, C 3.6471 and D 15. Now, when looking at a question like this, I see that we have a log of two numbers being multiplied by each other. So we can think of and recall different logarithmic formulas and rules that we have to see how we can mani manipulate this expression into something else. So I'm just gonna write a general formula for, in this case, the product rule of algorithms. So let's say you have blog of base B of a multiplying C that'll be equal to log of base B, OK plus log of base B of C. So that's just the general formula of the product rule of algorithms and looking at our equation and our expression. And comparing to the recall expression, we see that they gave us blog with no specified base. When this happens, that means that the base is 10. So if they don't write any base, that base will be 10, so that 10 will be the B in a recall expression. The 261 will be the A in our recall expression and the 17 will be the C in a recall expression. So using that information, let's rewrite the expression that we have. So it'll be log of plus log of 17. And now we can't do anything else. We, there's no other way to manipulate this other than using the product rule once again, just to go back to the multiplication expression that we had at the beginning. So that product rule of algorithms can be used back and forth. It work works either way. So what we have now the log of 261 plus the log of 17 will give us the same answer as the log of 261 multiplied by 17. So there's no other way that we can simplify this. So we're left with plugging this into our calculator and you can plug either expression in, they'll give you the same answer. So I'll write the calculator answer before rounding. And once you plug that into the calculator, it gives you the answer of 3. and so on. And they asked us for four decimal places, which means we have to stop it at the zero. And we see that the number after the zero is the number eight, which means we have to round up. So I'll uh I'll write the rounded answer now and that'll be 3.6471 after rounding up because of the eight. So that'll be our answer for this question or in this case, letter C 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(387 * 23)

Key Concepts

Logarithms

Properties of Logarithms

Approximation and Rounding

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