Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Combine the given expression into a single logarithm.$$^{1 / 2} \log x+2 \log y-3 \log z$$

$$\log \frac{\sqrt{x} y^{2}}{z^{3}}$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Campbell University

McMaster University

Idaho State University

Lectures

01:12

Rewrite each expression as…

00:56

01:21

Condense the expression to…

01:26

Simplify to a single logar…

01:09

00:34

02:33

Combine the given expressi…

01:32

Write logarithmic expressi…

01:20

01:36

Express as a single logari…

So we're looking at one half log of X. We're gonna do some the law of logs here to undo this problem and the order in what you do. This is important s so make sure you pay close attention and you don't have to worry about the base, the implied bases 10 throughout in this problem. But the whole premise is the law of logs is taking the numbers air in front. I call him coefficients. I don't know if that's what they technically are, but I think of numbers in front as being coefficients. You can move them to be exponents. So looking at log that you want to do this first, by the way to the one half plus log of why squared and the minus log of Z Cube. Well, if we're combining things as a log rhythm, it's important that you pay attention to the sign eso if we have a plus sign that makes that be combined using multiplication so multiplied by why squared? Now my students always get this confused. But when you are subtracting you on Lee, do the next one as a division. So you combine logs that are subtracted with divisions. So becomes the Cube Now. The only other thing to write down then is that we know that X to the one half power is equal to the square root of X. Um, pretty much every math teacher will expect you to do that. It's very important in math that you understand rational exponents. The only other trick I have to this is if you wanted to, you could actually change this to a plus sign and then make this a negative exponents. And then if you do that, though, you might want to show this step. So this is equivalent as well X to the one half. Why squared C to the negative third? Well, if you have a negative exponents, we move that into the denominator. So that's another trick. Thio Algebra manipulation. So that's a correct answer to quickly

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:47

A radioactive substance disintegrates at a rate proportional to the mass pre…

00:52

Determine the value of the logarithm without the use of a calculator.$$\…

02:15

If the cost equation in Exercise I is $C(x)=0.5 x^{2}+x+1,$ what price shoul…

01:39

A radioactive substance has a half-life of 47 years. (a) Determine its decay…

03:26

Given the points (2,6) and (4,12) determine the (a) linear function, (b) exp…

01:49

Determine the equation of the tangent line at the indicated $x$ -coordinate.…

01:58

If $0.5=e^{k},$ determine $k.$

01:19

Write the given expression in exponential format. $$\log 1 / 100=-2$$

05:29

Determine the derivative.$$x^{2} e^{2 x^{3} y^{2}}-2 e^{x}+3 e^{2 y}=3 x…

Show that any smooth even function has a relative extremum at its $y$ -inter…