Notes

 

Logarithmic Form & Exponential Form
\(\displaystyle \log_{b}m=x \,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\, b^{x}=m\)

 

 

Practice Problems

Express in Exponential Form

\(\textbf{1)}\) Write \(\log_{b}\frac{1}{5}=25\) in exponential form.

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The answer is \( b^{25}=\frac{1}{5} \)

 

\(\textbf{2)}\) Write \(\log_{4}x=2\) in exponential form.

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The answer is \( 4^{2}=x \)

 

\(\textbf{3)}\) Write \(\log_{b}25=2\) in exponential form.

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The answer is \( b^{2}=25 \)

 

\(\textbf{4)}\) Write \(\log_{3}9=x\) in exponential form.

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The answer is \( 3^{x}=9 \)

 

Express in Logarithmic Form

\(\textbf{5)}\) Write \(m^5=32\) in logarithmic form.

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The answer is \( \log_{m}32=5 \)

 

\(\textbf{6)}\) Write \(3^x=27\) in logarithmic form.

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The answer is \( \log_{3}27=x \)

 

\(\textbf{7)}\) Write \(2^4=x\) in logarithmic form.

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The answer is \( \log_{2}x=4 \)

 

\(\textbf{8)}\) Write \(x^{10}=100\) in logarithmic form.

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The answer is \( \log_{x}100=10 \)

 

 

See Related Pages\(\)

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

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

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

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

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

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

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

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