In Exercises 58–59, use common logarithms or natural logarithms a...

Question

In Exercises 58–59, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log4 0.863

Accepted Answer

Welcome back. I'm so glad you're here. We've got this log rhythm log base five of 15947 and we are to evaluate it And we can use a calculator which is great but when we typically use a calculator, it wants to use log base tin. It really, really wants it to be in this log 10 form. So what do we do? Well we're going to use the change of base property. So we were called from previous lessons that the change of base property for logarithms tells us that when we have any log with a base of B of em it equals log with the base of A. Of M divided by log again with the base of A. Of B. And what we can choose what we want our A to B. So let's use log 10 for R. A. So A equals 10 and we can get that to the base that our calculators are happiest in and now we're just going to identify R B. Well OK. RB equals five from up here. And our m our big number is 15,000 947. Which means we can now say that The log base 10 of 15947 divided by the log base 10 of five equals. And we ask our calculators to figure this out for us and we get a big long number 6.126. And so one but we only need it to three decimal places. So look at the third decimal place. Okay well that six says the two is going to round up, so we've got 6.13. We look at our answer choices and that matches with answer choice C. Well done, we'll catch you on the next one.

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