Question

considerando log5 7=a e log5 2=b, determine o valor de log49 1024

Answer 1

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$\Huge\boxed{\sf{\underline{Mudanc_{\!\!,}a~de~Base}}}\\\huge\boxed{\boxed{\boxed{\boxed{\boxed{\sf{\ell og_ba=\dfrac{\ell og_ca}{\ell og_cb}}}}}}}$

$\sf{\ell og_{49}1024=\dfrac{\ell og_51024}{\ell og_549}}\\\sf{\ell og_{49}1024=\dfrac{\ell og_52^{10}}{\ell og_57^2}}\\\sf{\ell og_{49}1024=\dfrac{\diagdown\!\!\!\!\!10\ell og_52}{\diagdown\!\!\!2\ell og_57}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{\ell og_{49}1024=\dfrac{5b}{a}}}}}}$