Problems

Graph the following logarithmic function. Then state the domain of the function.

\(\textbf{1)}\) \( f(x)=\log(x) \)

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\(\textbf{2)}\) \( f(x)=\log_{2}(x) \)

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\(\textbf{3)}\) \( f(x)=\log_{2}(x+2)+1 \)

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\(\textbf{4)}\) \( f(x)=2\log_{2}(x-1)-3 \)

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\(\textbf{5)}\) \( f(x)=\ln(x) \)

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\(\textbf{6)}\) \( f(x)=-\ln(x) \)

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\(\textbf{7)}\) \( f(x)=\ln(-x) \)

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\(\textbf{8)}\) \( f(x)=-\ln(-x) \)

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See Related Pages\(\)

\(\bullet\text{ Logarithmic Form & Exponential Form}\)
\(\,\,\,\,\,\,\,\,\log_{b}(a)=c \rightarrow b^c=a…\)

\(\bullet\text{ Evaluating Logarithms}\)
\(\,\,\,\,\,\,\,\,\log_{2}(8)…\)

\(\bullet\text{ Expanding Logarithms}\)
\(\,\,\,\,\,\,\,\,2\log_{b}(x)+\log_{b}(z)-5\log_{b}(y)…\)

\(\bullet\text{ Decibel Problems}\)
\(\,\,\,\,\,\,\,\,N_{dB}=10\log \left(\frac{P}{10^{-12}}\right)…\)

\(\bullet\text{ Earthquake Problems}\)
\(\,\,\,\,\,\,\,\,M=\log\frac{I}{10^{-4}}…\)

\(\bullet\text{ Domain and Range Logarithmic Functions}\)
\(\,\,\,\,\,\,\,\,f(x)=log(x) \rightarrow \text{Domain:} x\gt0… \)

\(\bullet\text{ Graphing Logarithmic Functions}\)
\(\,\,\,\,\,\,\,\,f(x)=log_{2}(x)\)

\(\bullet\text{ Solving Logarithmic Equations}\)
\(\,\,\,\,\,\,\,\,\log_{2}(5x)=\log_{2}(2x+12)…\)

\(\bullet\text{ Inverse of Logarithmic Functions}\)
\(\,\,\,\,\,\,\,\,f(x)=log_{2}(x) \rightarrow f^{-1}(x)=2^x\)