In Exercises 105–108, evaluate each expression without using a ca...

Question

In Exercises 105–108, evaluate each expression without using a calculator. log (ln e)

Accepted Answer

If I make the following expression Ln of log 10. So We first have log 10 in our apprentices log 10. Now we don't have a specific base given to us for the log. If we don't our base is always based in now we have the same base here as we do our eggs here. This is of the form log base B B to the power of X. Since we have the same base here of our log as the exponent, this is just equal to X. In other words log base 10 10 is just equal to one because we have 10 to the first. This turns into Ellen Log 10. Now which is what I one. The Ellen of one. We know also our Ln as log with base E. I'll say that equals why? Now if we use our exponential form of a log. If we have what base B. At C equals Y. This turns the exponential form B. Race to the Y equals X. So if you look here our bases E. Race to the Y equals R. X. Which is one. Now we want to find what number we're going to raise. E. By to equal what to give us. Why? Well any number raised to the power of zero is going to equal one. So we can say into the Y. Equal to E. To the zero. Or other words are Y equals zero. We cannot simplify any further. So our answer is zero for answer. C. Okay I hope to help you solve the problem. Thank you for watching Goodbye

In Exercises 105–108, evaluate each expression without using a calculator. log (ln e)

Key Concepts

Logarithms

Natural Logarithm (ln)

Properties of Logarithms

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