How do you evaluate log_6 ( 1296 )?

May 3, 2016

${\log}_{6} \left(1296\right) = 4$

Explanation:

${6}^{1} = 6$
${6}^{2} = 6 \times 6 = 36$
${6}^{3} = 36 \times 6 = 216$
${6}^{4} = 216 \times 6 = 1296$

${\log}_{b} \left(e\right) = k$ is equivalent to saying ${b}^{k} = e$

Therefore if ${6}^{4} = 1296$ then ${\log}_{6} \left(1296\right) = 4$