Question

Sabendo que log3 5 = m, calcule: a) log3 (1/5)
b) log5 3.
c) log5 (1/3)

Me ajudem pf!

Answer 1

Temos as seguintes informações:

--> $log_{_3}5=m$

--> $5=3^m$

a)

$log_{_3}\frac{1}{5}\\\\log_{_3}5^{-1}\\\\-1.log_{_3}5\\\\-1\;.\;m\\\\-m$

b)

$log_{_5}3=x\\\\3=5^x\\\\3=(3^m)^x\\\\3=3^{mx}\\\\1=mx\\\\x=\frac{1}{m}$

c)

$log_{_5}\frac{1}{3}=x\\\\log_{_5}3^{-1}=x\\\\3^{-1}=5^x\\\\3^{-1}=(3^m)^x\\\\3^{-1}=3^{mx}\\\\-1=mx\\\\x=-\frac{1}{m}$