Question

Find the value of $lo{g}_{2\sqrt{3}}1728$

Answer 1

Let $y=lo{g}_{2\sqrt{3}}\left(1728\right)$.

we know that $1728=64\times 24$

$(2{)}^6\times (\sqrt{3}{)}^6=(2\sqrt{3}{)}^6$

then

$y=lo{g}_{2\sqrt{3}}$ $(2\sqrt{3}{)}^6$

$y=6lo{g}_{2\sqrt{3}}$ $\left(2\sqrt{3}\right)$ $[lo{g}_{x}x=1]$

$[y=6]$.