Question

S=Log10 0,001+Log3 27-Log8 16

Answer 1

Resposta:

$S = - \dfrac{4}{3}$

Explicação passo-a-passo:

Detalhando:

$S = log_{10}(0,001) + log_{3}(27) - log_{8}(16) \\ S = log_{10}\left( \dfrac{1}{1000} \right) + log_{3}( {3}^{3} ) - \frac{ log_{2}(16) }{ log_{2}(8) } \\ S = log_{10}( {1000}^{ - 1} ) + 3. log_{3}(3) - \frac{ log_{2}( {2}^{4} ) }{ log_{2}( {2}^{3} ) } \\ S = log_{10}[( {10}^{3})^{ - 1} ] + 3.1 - \frac{4. log_{2}(2) }{3. log_{2}(2) } \\ S = log_{10}( {10}^{ - 3} ) + 3 - \frac{4.1}{3.1} \\ S = - 3. log_{10}(10) + 3 - \frac{4}{3} \\ S = - 3.1 + 3 - \frac{4}{3} \\ S = - 3 + 3 - \frac{4}{3} \\ \boxed{\boxed{S = - \frac{4}{3}}}$