SOLUTION: Describe the transformations that take the graph of f(x)=log4 x to the graph of g(x) = log4 x^3 = log4 8. Justify your response algebraically. equation orientation(s): https://g

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Describe the transformations that take the graph of f(x)=log4 x to the graph of g(x) = log4 x^3 = log4 8. Justify your response algebraically. equation orientation(s): https://g      Log On


   

Question 1205567: Describe the transformations that take the graph of f(x)=log4 x to the graph of g(x) = log4 x^3 = log4 8. Justify your response algebraically.
equation orientation(s): https://gyazo.com/ca5a482b67d375dd99cc56c691859ed6
https://gyazo.com/58bc03d93004990125826bcbf7dfc7e5
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=log%284+%2Cx+%29+ ...the parent function
g%28x%29+=+log%284%2C+x%5E3%29+-+log%284%2C8%29+
----------------------------------------

g%28x%29+=+3log%284%2C+x%29+-+log%284%2C8%29 .....log%284%2C8%29=3%2F2

g%28x%29+=+3log%284%2C+x%29+-+3%2F2

general formula transformed function in this case will be
g%28x%29=a%2Alog%284%2Cx%29-d

if a%3E1 , the graph is stretched by a factor of a; you have a=3
if d%3C0 we have vertical shift down d units: you have d=3%2F2

so we have
vertical stretch: stretched by factor+3++
vertical shift : down 3%2F2 units