Let $f(x) = 3 \ln{x}$ and $g(x) = \ln{5x^3}$. Express $g(x)$ in the form \(f(x) + \ln{a}\

Question

Let $f(x) = 3 \ln{x}$ and $g(x) = \ln{5x^3}$. Express $g(x)$ in the form $f(x) + \ln{a}$, where $a \in \mathbb{Z}^+$. The graph of $g$ is a transformation of the graph of $f$. Give a full geometric description of this transformation.

Accepted Answer

(a) $g(x)=f(x)+\ln5$, $a=5$ (b) translation by $\begin{pmatrix}0\\ln5\end{pmatrix}$

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions

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