In Exercises 41–70, use properties of logarithms to condense each...

Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator.

(1/2)(log x + log y)

Accepted Answer

Hello everyone in this video. We're going to be looking at this practice problem where we want to condense the equation 1/ times natural log a plus natural log B into a single algorithm with a coefficient of one. And we're going to try to condense or evaluate without using a calculator. So when we're trying to condense logarithms, it's important to remember logarithmic properties. So for example when we have two logarithms being added together, say I have natural log M plus natural log key and there's addition between them. I can combine this into a single algorithm using B. Product rule that says that when two are being added together, I can combine them into one by multiplying the value. So natural log M plus natural log K becomes natural log MK. And if we have say a times natural log M, I can get rid of this coefficient by making it an exponent of em. So eight times natural log M becomes natural log M to the power of A. And that is known as the power rule. So we're gonna use these rules to condense this equation into a single algorithm and make sure that the coefficient is one. So you can see that there's two sets of parentheses. We have the 1/4 and then the natural log A plus natural log B. So I'm going to work with the second set of parentheses where I have natural log a plus natural log B. So I have this edition. So I can use the product rule to combine this to be natural log A times B. And if I add in the first set of parentheses, I have a 1/4 and notice how we want a coefficient of one. So I have to make sure to move this 1/4 into the logo rhythm. So I can rewrite this using the power rule as natural, log A. B to the power of 1/4. And now you can see that I have a coefficient of one, so this becomes my final answer, and this answer aligns with answer choice B. So hopefully this video helped and see you next time.

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. (1/2)(log x + log y)