Question

se:
$log_{10}(225) = a$

então calcule:
$log_{10}( \sqrt[4]{ \sqrt[3]{(0.00225) ^{5} } } )$

Resposta:
$\frac{5a - 25}{12}$

Gostaria do passo a passo. Obrigado!!!
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Answer 1

$log_{10}(\sqrt[4]{\sqrt[3]{(0,00225)^{5}) } }\\log_{10}\sqrt[4.3]{(0,00225)^{5}} \\log_{10}\sqrt[12]{(0,00225)^{5}}\\log_{10}\((0,00225)^{\frac{5}{12} }\\\frac{5}{12} }log_{10}225.10^{-5}\\\frac{5}{12}(log_{10}225+log_{10}10)\\\frac{5}{12}(a+1)\\\frac{5a+5}{12}$