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Problems
Find the domain and range of the following logarithmic functions.
\(\textbf{1)}\) \( f(x)=\log(x) \)
\(\textbf{2)}\) \( f(x)=\log_{2}(x) \)
\(\textbf{3)}\) \( f(x)=\log_{2}(x+2)+1 \)
\(\textbf{4)}\) \( f(x)=2\log_{2}(x-1)-3 \)
\(\textbf{5)}\) \( f(x)=\ln(x) \)
\(\textbf{6)}\) \( f(x)=-\ln(x) \)
\(\textbf{7)}\) \( f(x)=\ln(-x) \)
\(\textbf{8)}\) \( f(x)=-\ln(-x) \)
\(\textbf{9)}\) \( f(x) = \log_2(x + 3) + 2 \)
\(\textbf{10)}\) \( f(x) = \ln(x + 1) – 1 \)
See Related Pages\(\)
\(\bullet\text{ Logarithmic Form & Exponential Form}\)
\(\,\,\,\,\,\,\,\,\log_{b}(a)=c \rightarrow b^c=a…\)
\(\bullet\text{ Evaluating Logarithms}\)
\(\,\,\,\,\,\,\,\,\log_{2}(8)…\)
\(\bullet\text{ Expanding Logarithms}\)
\(\,\,\,\,\,\,\,\,2\log_{b}(x)+\log_{b}(z)-5\log_{b}(y)…\)
\(\bullet\text{ Decibel Problems}\)
\(\,\,\,\,\,\,\,\,N_{dB}=10\log \left(\frac{P}{10^{-12}}\right)…\)
\(\bullet\text{ Earthquake Problems}\)
\(\,\,\,\,\,\,\,\,M=\log\frac{I}{10^{-4}}…\)
\(\bullet\text{ Domain and Range Logarithmic Functions}\)
\(\,\,\,\,\,\,\,\,f(x)=log(x) \rightarrow \text{Domain:} x\gt0… \)
\(\bullet\text{ Graphing Logarithmic Functions}\)
\(\,\,\,\,\,\,\,\,f(x)=log_{2}(x)\) 
\(\bullet\text{ Solving Logarithmic Equations}\)
\(\,\,\,\,\,\,\,\,\log_{2}(5x)=\log_{2}(2x+12)…\)
\(\bullet\text{ Inverse of Logarithmic Functions}\)
\(\,\,\,\,\,\,\,\,f(x)=log_{2}(x) \rightarrow f^{-1}(x)=2^x\)
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