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This worksheet allows you to play with the Change of Base Formula for Logarithms:
$$
\log_b\,x = \frac{\log_a\,x}{\log_b\,a}
$$
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Click anywhere in the GeoGebra window (at right) to make it active.
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Use the sliders to change:
- the base of the starting logarithm,
‘original base’:
$$
\log_{\LARGE \color{green}b}\,x = \frac{\log_a\,x}{\log_{\LARGE \color{green}b}\,a}
$$
- the base that you want to change to,
‘new base’:
$$
\log_{b}\,x = \frac{\log_{\LARGE \color{green}a}\,x}{\log_{b}\,{\LARGE \color{green}a}}
$$
- the input to the logarithm,
‘input to logarithm’:
$$
\log_{b}\,{\LARGE \color{green}x} = \frac{\log_{a}\,{\LARGE \color{green}x}}{\log_{b}\,{a}}
$$
- Refresh this page at any time to restore it to its initial configuration.
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