Question

Dado log2=0,3 e log3=0,5. Calcule log8 e log18

Answer 1

Explicação passo-a-passo:

$\bullet~\text{log}_{b}~a^{n}=n\cdot\text{log}_{b}~a$

a) $\text{log}~8=\text{log}~2^{3}=3\cdot\text{log}~2=3\cdot0,3=0,9$

$\bullet~\text{log}_{b}~(a\cdot c)=\text{log}~a+\text{log}~c$

$\text{log}~18=\text{log}~(2\cdot3^2)$

$\text{log}~18=\text{log}~2+\text{log}~3^2$

$\text{log}~18=0,3+2\cdot\text{log}~3$

$\text{log}~18=0,3+2\cdot0,5=0,3+1=1,3$