in-exercises-73-78-solve-the-equation-or-inequality-2-log-x-4-log-30

Question

In Exercises $73-78,$ solve the equation or inequality.
$2 \log x-4 \log 3>0$

Linh Vu · Accepted Answer

in this question Here, we need yourself the inequality. And in this question, I&#x27;m going to use, unlike Afrin calculator. In this count, the dead smalls in discussion here were given in in inequality and perform two terms. Lock off the X minus four times lock on the three and will be greater than zero. So the solution should be in the shade shop here, and he&#x27;ll edition, show us the X intercept here to figure it out. We grab the function f X equals, you know, to lock on the X minus phone lock on the three. And then it will be why you go to the zero. So it was him in here. This point will be intersection between the left hand side and the right hand side under inequality in equal to the nine. Therefore, it means that the solution, June, this inequality will be the interval from nine up to Infinity

Julian Wong · Answer

this problem won&#x27;t solve this inequality. So using the power rule in the first term, that&#x27;ll be four Log X minus three Log X and on the right side will use the question rules. A log of eight X over for X. That means Log X is less than log of two. So ah, since the basis are the same, we can see that X has to be less than two for this toe. Hold true.

Brianna Orr · Answer

solving the inequality wrong based to off drinks minus eight, which is greater than or equal to six because you know that the log off base B rex, which is greater than or equal to why, can be rewritten as X is greater than or equal to you. She raised her Why as long as B is greater than one on and X is good and zero by inequality trying. The solution for inequality can be phoned in or K&#x27;s or B is two or X is the X minus age on door. Why is equal to six? So we&#x27;re a solution, or inequality would build the form X, which is equal to three X miners. Eight is greater than or equal to be, which is to raise two. White, which is six. That simplifies to three X minus eight is greater than or equal Jew 64. Solving for X. We&#x27;re going to add egg so we have three X is greater than or equal to 64. Her eight. The X is greater than or equal to sarin teacher. If I didn&#x27;t buy three just off for X, we have X being greater than or equal to therefore this is going to help us find or solution, but we also need to take into consideration p the main aka luxury them on order Mean would be three X minus Age is greater than zero because the values for the longer than can&#x27;t be zero or negative writing that inequality, the X minus age is better than Jew. Going for X that would give us three X is greater than each and then X is greater than it&#x27;s Gracie going a number line. We have 8/3 other sport on 24 at this point. Thanks, it&#x27;s great. Another equal to 24. Those values tend to go this way on de CSIs, created on exes, grated on a chair with three. Those rallies would go there straight. Therefore over. And Angelo Israel, we have the common you shall not that you inequalities, which is as etc. Is greater than or equal to 24. Therefore, resolution ease X is greater than or equal to drink A for

Heather Zimmers · Answer

okay, If we have an absolute value inequality, we need to start by breaking it down into two different inequalities to remove the absolute value signs. It&#x27;s a way of three X squared minus seven. X plus. Two is greater than eight or three X squared minus seven x plus two is less than negative. Eight. Okay, now we have two different non linear inequalities to solve. So for the 1st 1 let&#x27;s subtract eight from both sides, and we have three X squared minus seven. X minus six is greater than zero. Let&#x27;s see if we can factor that. Okay, so we can try factoring it into three X and acts to give us three x squared. How about three times to to give us six? We do minus three plus two that will work. And then the numbers that make that equal to zero would be X equals negative 2/3 or X equals three. So those are the numbers we&#x27;re going to use to divide our number line into intervals? Yes, we have negative 2/3 and we have three. So the intervals are negative. Infinity to negative 2/3 and negative 2/3 to 3 on three to infinity. Okay, so now what we can dio is we can pick a number in each interval and test it to see if it makes this inequality greater than zero or less than zero. So suppose we test X equals negative one X equals zero and X equals four. So we take negative one. We substituted in here, we get a negative and in here we get a negative negative times. Negative is positive. Let&#x27;s take zero substituted in here. It&#x27;s positive. And here it&#x27;s negative. Positive times negative is negative. And for in here we get a positive and here we get a positive positive times. Positive is positive. So that means that this part is true when it&#x27;s greater than zero. And that is for this interval and this interval. So for this half of the problem we have X is an element of the interval from negative infinity to negative 2/3 Union three to infinity. Now let&#x27;s go back to the other half of the problem. So we need to add eight to both sides of this inequality to get a zero and let&#x27;s see if we can factor this. Okay, so if we have 10 times the one to give us 10. We have minus 10 and plus one that should work. And so the numbers that make this equal to zero that we&#x27;re going to use to divide our number line in intervals are 13th and negative one. So for this one, we have our number line. We have negative one, and we have 13th and so are intervals are negative. Infinity to negative one negative, 1 to 13th and 13th to infinity. Okay, so let&#x27;s pick a test number in each interval. Oops. What&#x27;s Pig X equals negative two. Let&#x27;s pick X equals zero and let&#x27;s pick X equals four. Okay, so testing into the factors starting with negative to who would get a negative times a negative, which is a positive. And now, with zero, it would get a negative times of positive, which is a negative. And for four we would get a positive times a positive, which is a positive. And for this one, we want it to be less than zero. So we want negative. Okay, so we have the interval from one from negative one to 13th. Now. There&#x27;s probably some overlap here. We have some overlap in this interval and this interval and because, um because negative one falls between these two numbers and we also have some overlap in this interval and this interval because 13th falls between those two numbers. So, actually, if we put this all together, let&#x27;s picture this on our number line. So here&#x27;s negative 2/3 and here&#x27;s negative one. And here&#x27;s three and here&#x27;s 13th. Okay, so we have all of these numbers. We have all of these numbers and we have all of these numbers, so we have the entire number line. So our answer is X is an element of the interval from negative infinity to infinity or, if you want to say all real numbers

Kimberly Moon · Answer

Okay, So given the a problem, a log obey seven X square plus 36 equals law. A seven of 100 one of the rules is if you have a log, just one log on each side. So you have a log on each side and they&#x27;re set evil to each other and they have the same base. Then you can drop the logs and said the numbers people to each other. So then at this point, I&#x27;m just going to solve it like I would a quadratic I&#x27;d subtract that 100 and I get explode minus 64. And then this is just a difference of square. So classy. X minus e equals zero, right differences square six square root put in front of square root but in the back, just like so. So we got our X plus eight equals zero. We&#x27;ve got X minus eight equals zero. So when I saw these, I get X equals negative age and X equals eight. So then, with this, you just need to make sure. Can this be a negative eight? And when I go back, keep it a plug down. Well, when I put in negative eight squared. I&#x27;ll get positive 64 it&#x27;s not right here. Has to be positive. So in this case, it would be all right. So we have X equals plus or minus eight.

Brianna Orr · Answer

solving long based you off three eggs minus five, which is greater than log based to off exper seven. Using the property for the inequality off bloggers make functions or expression is going to become three. X minus five is Greater Gun X plus seven. That&#x27;s because once you have the same logs on either side off the inequality sign, they would cancel. She&#x27;d be left with the argument off the lock solving for X. We&#x27;re going to add five to both sides so we end up with the X is gooder than thanks Circus 12 Andi subtracting X from both sides, you get two X is greater than off. Therefore, X is greater than six. But this isn&#x27;t o. R. And so we need to take into consideration where the domain off or loggers make function. Inter six X is greater than six. So what we take the log off? These must be cuter than Djourou. It can&#x27;t be Gina, and it can&#x27;t be negative. So creating or only any hard you With these, we would get three X minus five. Your X minus Phi Educated angina on eggs plus seven is greater than zero solving for X eggs is greater than 5/3 on eggs is greater than negative seven. The method that we used to determine where are until eyes is the number line. So we&#x27;re going to draw number line. Well, let&#x27;s put this were there dome. So here&#x27;s our number. Lay. We have negative seven. We over here. I have a fee right here and chicks will hair so x greater than six. I need to tend to go this way x rich and then I will with three values. Also 10. Judiciary Thanks greater than negative seven values and to go this way notice The common area for all our inequalities is from six. Therefore or answer is X is greater on six testing to see if this is true, we&#x27;re going to plug our number. That&#x27;s greater than six into or inequality using seven as X seventies. Greater 96 It becomes more three times seven, which is 21 minus by which is greater than love. These two of 14. This gives us love. These two of 16 he&#x27;s good in a long based to off 14 16 can be written as to race in the fourth hole. So this is long based to off to raising 1/4 boy, you should on log based you for 18 using the poor or four would they brought down on be placed in front of the log. So this should become for log beast True of to is greater than log to not based You know, for a team log based two off to is one because what a long is off is equal to the basin along. So this becomes for is greater than long a stool 14 using a calculator. Devaluate this expression we get it to be 3.8 on four is indeed greater than reprint. Ich sorry around it off. Increasingly, this is supposed to be on 3.81 therefore or un so proved to be great, which was ex being greater than six.

Problem

In Exercises $73-78,$ solve the equation or inequ…

Problem 77 Easy Difficulty

In Exercises $73-78,$ solve the equation or inequality.
$2 \log x-4 \log 3>0$

Answer

$x>9$

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Franklin D. Demana,Bert K. Waits,Gregory D. Foley,Daniel Kennedy

Precalculus: Graphical, Numerical, Algebraic

Grace H.

Catherine R.

Kayleah T.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

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$x>9$

Precalculus: Graphical, Numerical, Algebraic

Grace H.

Catherine R.

Kayleah T.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

Franklin D. Demana,Bert K. Waits,Gregory D. Foley,Daniel KennedyPrecalculus: Graphical, Numerical, Algebraic

Grace H.

Catherine R.

Kayleah T.

Caleb E.

Franklin D. Demana,Bert K. Waits,Gregory D. Foley,Daniel Kennedy

Precalculus: Graphical, Numerical, Algebraic