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

Question

In Exercises 21–42, evaluate each expression without using a calculator. log7 √7

Accepted Answer

Hey everyone in this problem we are asked to evaluate the following expression. The expression we're given is log base 11 of the square root of 11. Okay so writing that out log base 11 of the square root of 11. Okay now let's recall our log rules if we have log base B of something X. Okay. And let's make that equal to say why? Well we can rewrite that as be the exponent Y is equal to X. Okay so the base of the log becomes the base of the exponent. So in this case if we say why is equal to log base 11 of the square root of 11, Then we can rewrite this as 11 to the exponent Y. is equal to the square root of 11. Alright so now we have this and we know that if we can get the base the same on both sides will be able to compare the exponents. Okay so let's remember some exponent rules. If we have the end route of some value. M Well we can just write this as M. Two the exponents one over in. So using this rule we can rewrite that square root of 11 as 11 to the 1/2. Well now we have the same base on both sides of the equation. That means that the exponents must be the same. Okay so this tells us that why is equal to one half and again why is the value of that original expression log base 11 squared 11. So that's our answer and that's gonna be answer B. Thanks for watching everyone see you in the next video.

In Exercises 21–42, evaluate each expression without using a calculator. log7 √7

Key Concepts

Logarithms

Properties of Logarithms

Change of Base Formula

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