Question

Resolva Os Seguintes Logaritmos: a) Log8 32=x b) Log4 (Log3 9)

Answer 1

a)

$log_{_8}32=x\\\\\\32=8^x\\\\\\2^5=\left(2^3\right)^x\\\\\\2^5=2^{\,3\;.\;x}\\\\\\2^5=2^{3x}\\\\\\3x=5\\\\\\x=\frac{5}{3}$

b)

Nesta fica mais simples se resolvermos o log[3] 9 separado:

$log_{_3}9=a\\\\\\9=3^a\\\\\\3^2=3^a\\\\\\a=2$

Agora resolvemos a expressão:

$log_{_4}(log_{_3}9)=x\\\\\\log_{_4}(a)=x\\\\\\log_{_4}2=x\\\\\\2=4^x\\\\\\2=\left(2^2\right)^x\\\\\\2^1=2^{\,2\;.\;x}\\\\\\2^1=2^{2x}\\\\\\2x=1\\\\\\x=\frac{1}{2}$