Question

2) Com logx a = 5, logx b = 2 e logx c = -1, calcule:
a) logx(abc)
b) logx a^2 b^3 / c^4
(^ = expoente)

Answer 1

Explicação passo-a-passo:

Lembre-se que:

• $\sf log_{b}~(a\cdot c)=log_{b}~a+log_{b}~c$

• $\sf log_{b}~\Big(\dfrac{a}{c}\Big)=log_{b}~a-log_{b}~c$

• $\sf log_{b}~a^m=m\cdot log_{b}~a$

a)

$\sf log_{x}~(a\cdot b\cdot c)=log_{x}~a+log_{x}~b+log_{x}~c$

$\sf log_{x}~(a\cdot b\cdot c)=5+2-1$

$\sf \red{log_{x}~(a\cdot b\cdot c)=6}$

b)

$\sf log_{x}~\Big(\dfrac{a^2\cdot b^3}{c^4}\Big)=log_{x}~(a^2\cdot b^3)-log_{x}~c^4$

$\sf log_{x}~\Big(\dfrac{a^2\cdot b^3}{c^4}\Big)=log_{x}~a^2+log_{x}~b^3-log_{x}~c^4$

$\sf log_{x}~\Big(\dfrac{a^2\cdot b^3}{c^4}\Big)=2\cdot log_{x}~a+3\cdot log_{x}~b-4\cdot log_{x}~c$

$\sf log_{x}~\Big(\dfrac{a^2\cdot b^3}{c^4}\Big)=2\cdot5+3\cdot2-4\cdot(-1)$

$\sf log_{x}~\Big(\dfrac{a^2\cdot b^3}{c^4}\Big)=10+6+4$

$\sf \red{log_{x}~\Big(\dfrac{a^2\cdot b^3}{c^4}\Big)=20}$