Question

Dado log2 =30 , log5 =0,70 e log7 =0,85 calcule :

A) log50 na base 25

B) log8 na base 5

Answer 1

$\log_{}2=0,30$

$\log_{}5=0,70$

$\log_{}7=0,85$

A) $\log_{25}50= \dfrac{\log_{}50}{\log_{}25} = \dfrac{\log_{}5.10}{\log_{} 5^{2} } = \dfrac{\log_{}5+\log_{}10}{2.\log_{} 5 } = \dfrac{0,7+1}{2.(0,7) }= \dfrac{1,7}{1,4 }=1,21$

B) $\log_{5}8= \dfrac{\log_{}8}{\log_{}5} = \dfrac{\log_{} 2^{3} }{\log_{} 5 } = \dfrac{3.\log_{}2}{\log_{} 5 } = \dfrac{3.(0,3)}{0,7 }= \dfrac{0,9}{0,7 }=1,29$