Use properties of logarithms to rewrite each function, then graph...

Question

Use properties of logarithms to rewrite each function, then graph. ƒ(x) = log￬3 x+1/9

Accepted Answer

Rewrite the following logarithmic function using properties of logarithms. Then use a written function to graph it where we have what a six X plus two divided by 36. Now we can first make use of the quotient property of logarithms which states that if we have log, have the same base of M divided by N, this is equivalent to log of the same base M minus log base N. In other words, we can turn this into a attraction. You will have luck phase six X plus two minus log base six F 36. Now we can evaluate log base six of 36 in the calculator to give us log base six X plus two minus two. Now that we have a reflection, we can make a table of input and output values su plot onto our graph. See X and F of X, you notice we have an X plus two inside of our log function with lock functions. We cannot have a negative value or zero inside of our function. So we say X plus two equals zero or X equals negative two. That means our domain is a negative two to infinity. So we cannot have a number less than negative two or say negative two, negative 1.5, N 101 and two for possible points. Now let's plug these into our function F of negative two equals log base six, negative two plus two minus two. That gives us log space six of zero minus two, which is an undefined. Let's do the same with our next values. If we plugged in 1.5 negative here we get lo basics of negative 1.5 plus two minus two, which approximates to negative 2.39. We can now plug in the rest of our values negative two, negative 1. negative 1.39 and negative 1.23. Let's plot all of these on our graph. Now, as mentioned before, we cannot go past X equals negative two towards the left, which means we haven't pass in to right there at X equals negative two. We can now plot the rest of our points negative 1.5 and negative 2. native one native two zero, negative 1.61 one negative 1. 2 negative 1.23. We can now make a smooth curve between our points and following our, this is going downwards to the left. So we will draw a line from down there, going through our points flattening out as it goes up into the right. OK. I hope to help you solve the problem. Thank you for watching. Good bye.

Use properties of logarithms to rewrite each function, then graph. ƒ(x) = log￬3 x+1/9

Key Concepts

Properties of Logarithms

Change of Base Formula

Graphing Logarithmic Functions

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