Question

determine o valor das expressões.​

Answer 1

Usando as propriedades do logaritmo:

a)

2^(5log2 3)

2^(log2 3^5)

3^5

243

b)

2^(log7 7. log2 15)

2^(log2 15)

15

c)

(log5 10)^(log3 1)

(log5 10)^0

1

d)

(log64 64)^(log3 2)

1^(log3 2)

1

Resposta:

a) 243

b) 15

c) 1

d) 1

Answer 2

Explicação passo-a-passo:

Lembre-se que:

• $\sf b^{log_{b}~a}=a$

• $\sf log_{b}~a^m=m\cdot log_{b}~a$

• $\sf log_{a}~a=1$

• $\sf log_{a}~1=0$

• $\sf a^0=1$

• $\sf 1^n=1$

a)

$\sf A=2^{5\cdot log_{2}~3}$

$\sf A=2^{log_{2}~3^5}$

$\sf A=2^{log_{2}~243}$

$\sf \red{A=243}$

b)

$\sf B=2^{log_{7}~7\cdot log_{2}~15}$

$\sf B=2^{1\cdot log_{2}~15}$

$\sf B=2^{log_{2}~15}$

$\sf \red{B=15}$

c)

$\sf C=(log_{5}~10)^{log_{3}~1}$

$\sf C=(log_{5}~10)^{0}$

$\sf \red{C=1}$

d)

$\sf D=(log_{64}~64)^{log_{3}~2}$

$\sf D=1^{log_{3}~2}$

$\sf \red{D=1}$