Question

calcule os seguintes logaritmos:

a)log 2√2^64 = x

b)log 3√3^81 = x

c)log 3√3^243 = x

d)log 5∛5^625 = x

Answer 1

$a)\\\\log_{_2}\sqrt{2^{64}}~=~x\\\\\\\sqrt{2^{64}}~=~2^x\\\\\\2^{\frac{64}{2}}~=~2^x\\\\\\2^{32}~=~2^x\\\\\\\boxed{x~=~32}$

$b)\\\\log_{_3}\sqrt{3^{81}}~=~x\\\\\\\sqrt{3^{81}}~=~3^x\\\\\\3^{\frac{81}{2}}~=~3^x\\\\\\\boxed{x~=~\frac{81}{2}~~ou~~ 40,5}$

$c)\\\\log_{_3}\sqrt{3^{243}}~=~x\\\\\\\sqrt{3^{243}}~=~3^x\\\\\\3^{\frac{243}{2}}~=~3^x\\\\\\\boxed{x~=~\frac{243}{2}~~ou~~121,5}$

$log_{_5}\sqrt[3]{5^{625}}~=~x\\\\\\\sqrt[3]{5^{625}}~=~5^x\\\\\\5^{\frac{625}{3}}~=~5^x\\\\\\\boxed{x~=~\frac{625}{3}}$