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

Question

Use properties of logarithms to rewrite each function, then graph. ƒ(x) = log￬2 [4 (x-3) ]

Accepted Answer

Rewrite the following logarithmic function using are the properties of logarithms. Then use a written function to graph it where we have F of X equals log base 5 25 multiplied by X minus six. Now let's solve this. Let's first rewrite our function. We can first make use of the product property of logarithms, which tells us if we have a log, same base of M multiplying N inside the log, we can rewrite it as slug of M plus log of N. Other words, we can rewrite our log as lu base five of 25 plus log base five X minus six. We can also rewrite our log base 5 because we know 25 is five squared. We can use the product property of logs, which also tells us if we have luck base B B to the M that changes to M like base V of B like. So this means this transforms into two log base five of five. Bring down our other luck. And we notice we have log base five of five, which that turns into one. In other words, we have two plus log base five X minus six for our rewritten function. Now let's create a table of values to plot onto our coordinate plane. So we have X and F of X. Now, something we notice is that we have a log of X minus six. This means we have air force on a shift. The domain of the base log is from zero to infinity. And we're shifting this log by six units to the right because of our X minus six, this means our domain changes tipping from six to infinity. So we value is greater than six. We will say 6.5, 789 and 10. Let's plug these into the function F of six will give us two plus log base 56 minus six, which gives us two plus log base five of zero, which that is undefined, which makes sense because that is where our as to will be plus plug in 6.5. Next, that is two plus log base five, 6.5 minus six. If we were to approximate, we get about 1.57, we plugged in seven, we would get two, eight, you get 2.43 and so on 2. point 86. Now we have a list of values we can plug in because our domain is from six to infinity. And the base log has an ascent to, we will have an Asymptote at X equals six. Now, we can put the rest of our points 6.5, 1.57 72, 82.43 92.68, 10, 2.86. We can now make a smooth curve that follows our points and the ascent to starting from the bottom left, we follow the S and to till we get our point, go through all the points and head up into the right. And that gives us our graph for this problem. Ok. I hope to help you solve the problem. Thank you for watching. Goodbye.

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Use properties of logarithms to rewrite each function, then graph. ƒ(x) = log￬2 [4 (x-3) ]