contestada

Which of the following is equivalent to \log_4(m)\cdot \log_{m}(20)log
4
​
(m)⋅log
m
​
(20)log, start base, 4, end base, left parenthesis, m, right parenthesis, dot, log, start base, m, end base, left parenthesis, 20, right parenthesis ?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
555

(Choice B)
B
808080

(Choice C)
C
\log(5)log(5)log, left parenthesis, 5, right parenthesis

(Choice D)
D
\log_{4}(20)log
4
​
(20)

Respuesta :

Answer:

D.

[tex] log_4(20) [/tex]

Step-by-step explanation:

Remind the following properties:

[tex] log_a(b) = \frac{1}{log_b(a)}[/tex]

[tex] log_a(b) = \frac{log_c(b)}{log_c(a)} [/tex]

We are asked to simplify:

[tex] log_4(m) \cdot log_m(20) [/tex]

Using the first property:

[tex] \frac{1}{log_m(4)} \cdot log_m(20) [/tex]

[tex] \frac{log_m(20)}{log_m(4)}[/tex]

Using the second property:

[tex] log_4(20) [/tex]

Otras preguntas