Question

Sabendo que log3=0,47 determine o logaritmo de 10 na base 3

Answer 1

Log de 3 = 0,47 

Log 10 base 3 será? 

aplicando a propriedade de logaritimos temos 

Log10(3)=x 
Log10=3^x 
Log10=Log3^x
1=xLog3
1=0,47x
x=1/0,47
x=2,12  aproximado

Answer 2

$\mathsf{Mudan\c{c}a~de~base:~\large\fbox{ \mathsf{\ell og_{\beta}~\alpha=\dfrac{\ell og_c~\alpha}{\ell og_c~\beta}} }}\\\\\\\\\mathsf{Tomando~log~3=0,47~podemos~realizar~a~seguinte~rela\c{c}\~ao:}\\\\\\\mathsf{\ell og_3~10~\Leftrightarrow~\dfrac{\ell og~10}{\ell og~3}}\\\\\\\mathsf{\approx~\dfrac{1}{0,47}}\\\\\\\mathsf{\approx~2,12}~~~~\checkmark\\\\\\\mathsf{Obs:~a~base~est\'a~impl\'icita,~pois~\'e~decimal~(\ell og~{10}=\ell og_{10}~10=1).}$