New Notes Blog: `27^(2/3) = 9` Write the exponential equation as a logarithmic equation or vice versa

Friday, 20 February 2015

$\displaystyle{{27}}^{{\frac{{2}}{{3}}}}={9}$ Write the exponential equation as a logarithmic equation or vice versa

Take note that if the exponential equation is in the form

$\displaystyle{y}={{b}}^{{x}}$

its equivalent logarithmic form is

$\displaystyle{x}={\log}_{{b}}{\left({y}\right)}$

Thus, converting

$\displaystyle{{27}}^{{\frac{{2}}{{3}}}}={9}$

to logarithmic form, it becomes

$\displaystyle\frac{{2}}{{3}}={\log}_{{27}}{\left({9}\right)}$

Take note that if the exponential equation is in the form

$\displaystyle{y}={{b}}^{{x}}$

its equivalent logarithmic form is

$\displaystyle{x}={\log}_{{b}}{\left({y}\right)}$

Thus, converting

$\displaystyle{{27}}^{{\frac{{2}}{{3}}}}={9}$

to logarithmic form, it becomes

$\displaystyle\frac{{2}}{{3}}={\log}_{{27}}{\left({9}\right)}$

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