Question

Resolva a equação: log2(x - 2) = 5​

Answer 1

Resposta:

log₂ (x - 2) = 5​

(x-2)=2⁵

x-2=32

x=34

Answer 2

$\large\boxed{\begin{array}{l}\underline{\rm D~\!\!efinic_{\!\!,}\tilde ao~de~logaritmo}\\\sf \ell og_ba=x\Longleftrightarrow b^x=a\begin{cases}\sf a>0\\\sf b>0\\\sf b\ne1\end{cases}\\\sf \ell og_2(x-2)=5\\\underline{\rm Condic_{\!\!,}\tilde ao~de~exist\hat encia\!:}\\\sf x-2>0\implies x>2\\\sf\ell og_2(x-2)=5\\\sf x-2=2^5\\\sf x-2=32\\\sf x=32+2\\\sf x=34\\\sf como~34>2~ent\tilde ao\\\sf S=\{34\}\end{array}}$