Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 387 + log 23

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Hello everybody. I hope you're 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 the four decimal places, now, the expression that they give us is log of 411 plus log of 47. And the answer choices that they provide us are a 4.2859 B 3.9 oh 52 C 2.3341 and D 11. Now, we looking at a question like this, we see that we have two logs of the same base adding each other. And we have to ask ourselves, are there any rules for logarithms that we can use for this to maybe help us simplify the expression and make the question a little easier. And when we have two logarithms adding each other, there is uh the product rule which we can recall. And I'll write it down uh general formula for that which is blog of ba base B of A plus log of base B of seeing will be equal to log of base B of a multiplying C. Now, when comparing this to the equation that we have, when we have log with no other specified base, we can assume and we will know that that base will be 10. So the base in our expression is gonna be 10. So that 10 will be represented by the B in the recall. 411 will be the A in the recall and 47 will be the scene in a recall. So using that recall expression, let's rewrite this as the product to using the product tool. And we'll have log of 411 multiplied by 47. And that's all we can do here. There is no nothing else that we can simplify, we can go any further. So these two expressions log four of 411 plus log of 47 is the same as log of 411 multiplied by 47. So you could plug either of them into your calculator. But once you do that, I'll write down the calculator answer. Once you plug either of those into the calculator, it'll give you an answer of 4.285, 93 and so on. And they asked us to run to four dozen places. So we have to stop it at the nine. So the number that comes after the nine is a three, therefore, we don't have to round up. So our answer remains as 4. or in this case letter A 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 + log 23

Verified Solution

Key Concepts

Properties of Logarithms

Common Logarithm

Approximation and Rounding