Question

Calcule aplicando a propriedade:

A. $log_{\sqrt[5]{2} } 1024=x$

b.$log_{\sqrt[5]{2} } 256=x$

c.$log_{\sqrt{5} } y=2$

Answer 1

Resposta:

A)

$(\sqrt[5]{2} )^x=1024\\ \\ (2^{1\over5})^x=2^{10}\\ \\ 2^{x\over5}=2^{10}\\ \\ cancela~~base~~2\\ \\ {x\over5}=10\\ \\\boxed{ x=50}$

B)

$(\sqrt[5]{2} )^x=256\\ \\ (2^{1\over5})^x=2^8\\ \\ 2^{x\over5}=2^8\\ \\ {x\over5}=8\\ \\ \boxed{x=40}$

C)

$(\sqrt{5} )^2=y\\ \\\boxed{ y=5}$