Created on 2024-06-20Asked by Owen Gonzalez (Solvelet student)
Graph the logarithmic function f(x)=log3(x) and identify its domain and range.
Solution
To graph the logarithmic function f(x)=log3(x), we need to understand its properties. The logarithmic function f(x)=log3(x) has the following characteristics: - **Domain**: The set of all positive real numbers, (0,∞). - **Range**: The set of all real numbers, (−∞,∞). Here is the graph of the function: \begin{center} \begin{tikzpicture} \begin{axis}[ axis lines = middle, xlabel = x, ylabel = f(x), domain=0.1:10, samples=100, xmin=0, xmax=10, ymin=-2, ymax=3, width=10cm, height=8cm, grid=both, major grid style={line width=.2pt,draw=gray!50}, minor grid style={line width=.1pt,draw=gray!20}, ytick={-2,-1,0,1,2,3}, xtick={1,3,5,7,9}, ] \addplot[domain=0.1:10,blue,thick] {ln(x)/ln(3)}; \end{axis} \end{tikzpicture} \end{center} Therefore, the domain of f(x)=log3(x) is (0,∞) and the range is (−∞,∞). Solved on Solvelet with Basic AI Model
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DefinitionThe logarithmic function is the inverse of the exponential function. They are expressed as f x = log o g b – ( x ), where b is the base. Research notes dsax-x: A plugin function that allows us to retrieve values from x to b. For example, f x = l o g 2 – x means 2 f x = x; This is useful for transformation and base change. The natural logarithm is lnx log ex(x).
