Question

Given the functions 𝑓(𝑥) = 𝑙𝑜𝑔_3 (3𝑥) and 𝑔(𝑥) = 𝑙𝑜𝑔_3 (𝑥) + 1
a. Describe the transformations applied to each function.
b. How do the graphs of the two functions compare? Explain your answer by referring to logarithmic
laws and properties.

Answer 1

log3(3x) = log3(3) + log3(x) = 1 + log3(x)
f(x) is identical to g(x)

g(x) is f(x)
dilated in x by 3
shifted up 1
The two transformations cancel each other out

the graphs of all exponential functions look the same
dilating and shifting are complementary operations.