Question

Determine X tal que X = log 25 na base 7
(vezes) log 7 na base 5.

Alguém ajuda.

Answer 1

$x=\mathrm{\ell og}_{7\,}25\,\cdot\,\mathrm{\ell og}_{5\,}7\\ \\ x=\mathrm{\ell og}_{7\,}25\,\cdot\,\dfrac{1}{\mathrm{\ell og}_{7\,}5}\\ \\ x=\dfrac{\mathrm{\ell og}_{7\,}25}{\mathrm{\ell og}_{7\,}5}\\ \\ x=\dfrac{\mathrm{\ell og}_{7}\left(5^{2} \right )}{\mathrm{\ell og}_{7\,}5}\\ \\ x=\dfrac{2\mathrm{\,\ell og}_{7\,}5}{\mathrm{\ell og}_{7\,}5}\\ \\ x=2$