In Exercises 21–42, evaluate each expression without using a calc...

Question

In Exercises 21–42, evaluate each expression without using a calculator. log2 (1/√2)

Accepted Answer

welcome back. I'm so glad you're here. We are given the expression log base five of one divided by the square root of five. And we are asked to evaluate this. Well we recall from previous lessons that we are to ask ourselves the question five. This base raised to what power equals what we're taking the log of one divided by the square root of five. Alright well both sides have a five on them. Let's see if we can do some work with the right hand side of the equation to get that looking like five raised to an exponent. Will we recall from previous lessons on exponents that this square root of five? The square root can be rewritten as the exponents one half. So we can take the square to five and change that to five raised to the one half. That's closer. Now in order to get that five to the one half out of the denominator we can flip the sign of its exponent. So this would be five raised to the negative one half and there we go. That is looking like a five raised to an exponent. So now we've got five raised to the what? Equ five raised to the negative one half. Well that is five raised to the negative one half. Therefore log base five of one divided by the square to five is negative one half. We look at our answer choices and that matches with answer choice. D. Well done. We'll catch you on the next one

In Exercises 21–42, evaluate each expression without using a calculator. log2 (1/√2)

Key Concepts

Logarithmic Functions

Properties of Logarithms

Change of Base Formula

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