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. log5 (1/5)

Accepted Answer

Hello. Today we're going to be evaluating a logarithmic expression without using a calculator. So the logarithmic expression given to us is the log base of two of 1/8. And we're gonna go ahead and rewrite this values in a calculator. But let's recall that log base of A. Of B. Is equal to see this statement could be rewritten as a race to the power of C equal to B. So in order to rewrite this statement, all we did was take this log base of a raise it to the power of C. And now we have this new statement and we're gonna go ahead and do this here. So in order to start this process let's go ahead and set our logarithms equal to some arbitrary constant C. Now what we want to do is take our base of two and raise it to the power of C. So that we may get a statement in this format Doing so is going to give us to raise to the power of c equal to 1/8. Okay now what we wanna do is go ahead and rewrite this 1/8 as an exponent with base too. But how do we do that if this is a fraction? Well keep in mind that 1/8 can be rewritten as eight raised to the power of negative one. So we need to go ahead and rewrite this first to raise to the power of C. Is going to equal to eight, raised to the power of negative one. And keep in mind eight Is the same thing as saying two raised to the power of three. So rewriting the right hand side of this equation one more time is going to give me two to the power of C equal to two cubed Race the power of -1. And now that we have both the sides of this equation with the base of two, we can set the exponents equal to each other. Doing so is going to give me C equal to three times negative one. And multiplying three and negative one together is going to give me negative three. So C. Is equal to negative three. And that is going to be my solution. That also means that the solution to this problem is going to be a So I hope this video helps you in understanding how to rewrite a law algorithm without a calculator. And I'll go ahead and see you all in the next video.

In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log5 (1/5)

Key Concepts

Logarithms

Change of Base Formula

Properties of Logarithms

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