In Exercises 71–78, use common logarithms or natural logarithms a...

Question

In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places.

log14 87.5

Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where we want to evaluate the expression log base eight of 91.5. In order to evaluate this expression, we need to change it into a common lawyer rhythm Because most calculators assume log based 10. So we need to go from log base 8 to log base 10. Because we're changing from 8 to 10 we need to use the change of base property and the change of based property allows us to go From one base to another. And because we can't evaluate base eight we need to change into base 10. The change of base property sets that if we have say log base B. To the power of M. We can change that to log base A. With a division where we have log base A. Of M divided by log base A. Of B. So notice how the unwanted base B. Is in the denominator. So we're going to use this property to help us convert from log base eight into log base 10 so that we can evaluate the expression in our calculator. So in this case log base eight of 91.5 becomes log base 10 of 91.5 divided by log base 10. And the unwanted base in the denominator Log Base 10 of eight. So now we have this fraction where we have two logarithms Log Base 10 of eight and Log Base 10 of 91.5. But we can evaluate that in our calculator. And if we do that log base 10 of 91.5 is 1.96142. And that's still being divided by log base 10 of eight, which is 0.90309. And if we do this division, we get that log base eight of 91.5 is approximately 2.1719. So notice how we started with log base eight, we converted to 10 and then we evaluated in the calculator and we got an approximate answer of 2.1719. And that aligns with answer choice D. So hopefully this video helped and see you next time.

In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log14 87.5

Key Concepts

Logarithms

Change of Base Formula

Calculator Functions

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