Question

Determine o logaritmo operando a mudança de base (também utilizando os valores dos log’s dados da tabela):
a) log6 25
b) log3 12

Answer 1

a)

$\mathsf{\ell og_{6}25=\dfrac{\ell og25}{\ell og6}=\dfrac{\ell og5^2}{\ell og2.3}}$

$\mathsf{\ell og_{6}25=\dfrac{2\ell og5}{\ell og2+\ell og3}}\\\mathsf{\ell og_{6}25=\dfrac{2\ell og(\frac{10}{2})}{\ell og2+\ell og3}}$

$\mathsf{\ell og_{6}25=\dfrac{2\ell og10-2\ell og2}{\ell og2+\ell og3}}$

$\mathsf{\ell og_{6}25=\dfrac{2.1-2.0,3}{0,30+0,47}}\\\mathsf{\ell og_{6}25=\dfrac{2-0,6}{0,77}=\dfrac{1,4}{0,77}}$

$\boxed{\boxed{\boxed{\boxed{\mathsf{\ell og_{6}25=\dfrac{20}{11}}}}}}$

b)

$\mathsf{\ell og_{3}12=\dfrac{\ell og2^2.3}{\ell og3}=\dfrac{2\ell og2+\ell og3}{\ell og3}}$

$\mathsf{\ell og_{3}12=\dfrac{2.0,30+0,47}{0,47}}$

$\mathsf{\ell og_{3}12=\dfrac{0,6+0,47}{0,47}=\dfrac{1,07}{0,47}}$

$\boxed{\boxed{\boxed{\boxed{\mathsf{\ell og_{3}12=\dfrac{107}{47}}}}}}$