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

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

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

Logarithmic Functions

Oregon State University

McMaster University

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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'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'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'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'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

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