Question

Alguém pode me ajuda com esse cálculo a) log 16 64

Answer 1

Dada a propriedade logaritmântica:

$\mathsf{\log _b\left(a\right)=c\:\:\:\:\Longleftrightarrow \:\:\:\:b^c=a}$

= = = = =

Logo:

$\mathsf{\log _{16}\left(64\right)=x}\\\\\mathsf{16^x=64}\\\\\mathsf{\left(4^2\right)^x=4^3}\\\\\mathsf{4^2^x=4^3}\\\\\mathsf{2x=3}\\\\\boxed{\mathsf{x=\dfrac{3}{2}}}\: \: \checkmark$