Question

Determine o valor de N quando : N=3 . log4 64 - 5 . log5 125

Answer 1

$\Large\fbox{ \mathsf{N=3\ell og_4~64-5\ell og_5~125} }\\\\\\\mathsf{\ell og_4~64 =x~~\Leftrightarrow~~4^x=64~~\Leftrightarrow~~4^x=4^3~~\Leftrightarrow~~x=3}\\\\\mathsf{\ell og_5~125=y~~\Leftrightarrow~~5^y=125~~\Leftrightarrow~~5^y=5^3~~\Leftrightarrow~~y=3}\\\\\\\mathsf{N=(3\ell og_4~64-5\ell og_5~125)}\\\\\mathsf{N=3x-5y}\\\\\mathsf{=(3\cdot 3)-(5\cdot 3)}\\\\\mathsf{=9-15}\\\\\mathsf{=-6}\\\\\\\large\fbox{ \mathsf{\therefore~N=-6} }$