the-function-fxlog-_9-x-is-the-logarithm-function-with-base-________-so-f9__________-f1_________-fle

Question

The function $f(x)=\log _{9} x$ is the logarithm function
with base ________. So $f(9)=$__________,
$f(1)=$_________, $f\left(\frac{1}{9}\right)$ $f(81)=$__________, and $f(3)=$______.

Erna Bisschoff · Accepted Answer

But in this question it states that the function if X that is given by log nine X is longer than function with bass off Arent ear. Then nine is the base good. So the nine that&#x27;s like a footnote in the locker room. He is the base off the logarithmic function, so that if off nine is equal to lock, So in the place of the ex, we put nine. And this is a law that if the base and this value is equal, then the whole lock becomes one right? And for one, if I put it in the eggs, this is zero, right? But let&#x27;s see why I can change the one into nine to the power off zero, right? And now I have a law that state that if I have a log, a be too far off, see, then the sea can come to the front and multiply with the whole lock writer. That&#x27;s the law. So if I apply this law in here, they becomes zero times the log nine off nine, which is then zero. So remember this. Any log with a one is equal to zero and four is won over nine into X. So I&#x27;m going to rewrite the 1/9 in its exponential form. So it becomes nine to the power of negative one. Now the negative one for that same law, Yeah, can come to the front and multiply with the whole lug off base nine and nine, which is one. So my final on Sunday is negative one. Then, for if off 81 I can put the 81 in day and I can rewrite the 81 in terms off nine. You might want to write it in the prime factors, but in this case, because the base is equal to nine, I would rather rewrite the 81 as nine squid, following the same rules as previously. This will give me two log 99 which is equal to two. And finally, for if off three. That means we substitute three into the eggs and three is the same as this squared off nine, right? And the square it off nine is actually nine to the power off 1/2. Bring the half to the front. My final answer is just whenever, too

Aamir Mithaiwala · Answer

So with this problem we have a log based nine. So our base here is nine. And so if we wanted to find f of some values Well, all we have to do is plug in plugging that value for X. So our first problem we have X is equal to nine. So if we rewrite this and say we have we have nine to the X is equal to or nine to some unknown. Let&#x27;s say this unknown. Let&#x27;s change f of X to be a well. The nine of a is equal to nine and so a is equal to once so is equal to one. And then now, if we have X is equal to zero, well, nine to the zero is equal to one or rather it. This would be this would be X to the one here we&#x27;re asked for X is equal to one, so we would have nine to the A is equal to one. Well, then a is equal to zero. So for our next one we have, we have X is equal to we have X is equal to this value. 1/9 here one overnight and so we have nine to the A is equal to one over night. Well, then well, then A is equal to negative one. And so now we have X is equal to X is equal to anyone. So nine to the A is equal to 81. Well, then A is equal to you too. So So now we have X is equal to X is equal to three. We have nine to the A is equal to three. Well, if a is 1/2 if a is equal to 1/2 then we have the square root of nine, which is three. And so our values here are 10 negative one. So our values here are Remember our bases nine and then we have one zero negative. One 10 negative 12 and 1/2. Two and 1/2. And so these our solutions Remember, this nine is our base and these are our values of FX. Remember we said Don&#x27;t let it confusing. We just said f of X is equal to a

Katelyn Chen · Answer

for this question. We know that log nine of X is base nine. So we know that off of nine is equal to just simply one. You&#x27;re off of one people to zero. We know off of one night is equal to negative one. Well, after really one, it&#x27;s simply equal to two because nine scored is just too, and then we have a 1st 3 is equal to 1/2 so these are answers.

Ankit Gupta · Answer

in the group in question, affecting the acquittal log X Basie. And it is given that f off three is equal Toto. So if you will find F or three, this will be called to log off three Basic and it is given us to so three can be written as a square. Are you considered it will be Quito plus or my nephew or three, but negative base kind of a negative. So able Very Quito, Route three. Hence, we can say that funds will be long X based on all three. Now we will have to find the value off their fourth one by nine. In the fourth part, F off one by nine will be called a log off one by nine based on your three. So one by nine candidate and has three to the power minus two and two or three can be written as three to depart one bite. So this will be acquittal minus four. No. In the second part of the question, we have to find the value off. Log off 27 so this will be called to log off 27 based Route 3 27 Can bitterness three Cube and roar three can be return estatal de part one by toe. So this will be quite to six. Now, we also have to find the value off F inwards off minus two as well. A deaf in works of Jiro. So we will have to calculate the value or effort were forced full effects these log X based report three. So basically why is equal to log X base or three now to find the inverse we will have to in Turkey in X and y so we can write excessive quick Oh, love, why way through three Now we will have to calculate why so I will be quite a rook three to the Power X. So this is defense on F inverse X, which is equal to three to the power X by toe now. So in the fourth part of the or the second part of the question, we have to find the value off everyone worse off my next. Oh, so this will be a little three to the power minus two by two, which is equal to three to depart minus one which is equal to one upon three. And in the last part of the question. We have to find the value off effin worth of Jiro, which is equal to three to the power tear open toe, which is equal to three to the power deal, which is equal to one.

Amy Jiang · Answer

Okay, So asked about it after 81. We have law three of 81. So that means that 32 parts something is equal to 81. Well, let&#x27;s make anyone with the base of 3 to 3. To what power gives this 81. That&#x27;s 3 to 4. So we see that this question mark must be equal to four, which is equal to so our log is equal to four.

Benjamin Schreyer · Answer

So we&#x27;re given a function that takes an value X and gives you back what exponents you have to raise nine to. To give Exxon example would be f of nine equals one because you have to raise nine to the first to get nine, which is what we gave it. Another example could be f of 81 equals two because nine to the two equals 81. So were then asked to find the values for each. So we need to find f of one. So we know that 9 to 0 equals one. So we know that f of 10 way find f of 7 29 and we&#x27;re just gonna do this by guessing that nine to the three and we&#x27;re going to see what nine to the three equals. Going into a calculator, we get 7 29 which means that this one will be equal to three f of 7 29 f in verse of to. So we need to find what would our inverse B. So if it if the normal function af gives takes a number and gives the exponents that goes on nine, then are inverse will taken exponents and put it on nine so we can check that that works so we can try F in verse of zero equals 9 to 0 equals one. We can check EC F in verse of three equals nine to the three equals 7 29 So are inverse F in verse of ax equals nine to the X. So we know f inverse of two is gonna be equal to 81 and f in verse of 1/2 is going to be the square root of 99 to the 1/2 which is gonna be equal to three.

Problem

\begin{equation}\begin{array}{l}{\text { (a) } 5^…

Problem 2 Medium Difficulty

The function $f(x)=\log _{9} x$ is the logarithm function
with base __. So $f(9)=$,
$f(1)=$_, $f\left(\frac{1}{9}\right)$ $f(81)=$, and $f(3)=$.

Answer

$$
\begin{array}{ll}{f(9)=1} & {f(1)=0} \\ {f(81)=2} & {f(3)=0.5}\end{array}
$$

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$$\begin{array}{ll}{f(9)=1} & {f(1)=0} \\ {f(81)=2} & {f(3)=0.5}\end{array}$$

Algebra and Trigonometry

Grace H.

Heather Z.

Alayna H.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

James Stewart, Lothar Redlin, Saleem WatsonAlgebra and Trigonometry

Grace H.

Heather Z.

Alayna H.

Maria G.

$$
\begin{array}{ll}{f(9)=1} & {f(1)=0} \\ {f(81)=2} & {f(3)=0.5}\end{array}
$$

James Stewart, Lothar Redlin, Saleem Watson

Algebra and Trigonometry