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 [9 (x+2) ]

Accepted Answer

You write the following logarithmic function using the properties of logarithms. And then use a written function to wrap it where we have F FX equals line by seven of 3 43 multiplied by X plus four. Let's first use our properties of logs to rewrite our equation. One property is the product property which tells us if we have log base B of M multiplying N, we can rewrite it as log base B M plus log base B M, which we can rewrite this as log base 73 plus log base seven X plus four. We can now evaluate log base seven at 3 43. We put that in the calculator, we should get three, bring down our log base seven X plus four. And that gives us our rewritten formula. No, let's find input and output values to graph on our plane. We have X and we have F of X. Now we notice here we have log base seven X plus four. The domain of a log function normally goes from zero to infinity. But now we're shifting to the left by four based on our X plus four. This means our domain shifts from zero to infinity to negative four to infinity, which means we will have an ascent to and X equals negative four. I'll make a few other possible values all the way until we get to zero. Now, let's plug in these values into our equation. If you plugged in negative four, you'll get three plus log there. Seven negative four plus four says three plus log base seven of zero. That isn't on the fact, let's say we choose negative 3.5. Next. That is three plus log base seven, negative 3.5 plus four. If we were to simplify that we get about 2.64, let's plug in the rest of our values. We get three, three points 36, 3.56 and 3.71. We cannot plot all of these values onto our graph. Now, we have an ascent to at X equals negative four, which is denoted by the dotted line here. We cannot graph all of our points N 3.5, 2.64, negative 33, 82 3.36 13. N 3.71. Now, we just have to make a smooth curve that goes through all of our points and follows the ascent. Since we're going down to the left, we will start from down here, follow the ascent to hit the point and then curve upwards to the right, which gives us the graph of this function. OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Use properties of logarithms to rewrite each function, then graph. ƒ(x) = log￬3 [9 (x+2) ]

Key Concepts

Properties of Logarithms

Change of Base Formula

Graphing Logarithmic Functions

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