In Exercises 19–29, evaluate each expression without using a calc...

Question

In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. ln e^5

Accepted Answer

Hello today we're going to be evaluating a natural logarithmic expression without using a calculator. So the natural law given to us is the natural log of E. raised to the power of 71. So how do we start evaluating this? Well, let's go ahead and just recall one of our natural logarithms rules. We have a power rule which states that if we have the natural log of X raised to the power of N, we can take this exponents and move it to the front of the natural log as a product. So we can rewrite this as N times the natural log of X. And this is what we're going to do to evaluate this. So in this case here we're gonna let our end equal to 71. All we're going to do is take 71 move it to the front of this natural logarithms as a product. Doing so is going to give me 71 times the natural logarithms of E. And recall that the natural logarithms of E is equal to one. So replace the natural log of E with one is going to give us 71 times one. And that is going to equal 71, which will be our solution. That also means that the solution to this problem is going to be be So I hope this video helps you in rewriting natural logs without a calculator and I'll go ahead and see you all in the next video

Watch next