swagger1035
swagger1035 swagger1035
  • 02-12-2019
  • Mathematics
contestada

what value of n solves the equation 2n =1/8

A. -3
B. -4
C. 3
D. 4​

Respuesta :

rani01654 rani01654
  • 09-12-2019

Answer:

n = - 3

Step-by-step explanation:

We have to solve the equation [tex]2^{n} = \frac{1}{8}[/tex] for n.

Now, as the variable is in power, we will take a log on both sides.

So, [tex]2^{n} = \frac{1}{8}[/tex]

⇒ [tex]\log 2^{n} = \log \frac{1}{8}[/tex]

⇒ n log 2 = log 1 - log 8 {Since we know the property of logarithm [tex]\log a^{b} = b \log a[/tex] and [tex]\log \frac{a}{b} = \log a - \log b[/tex]}

⇒ n log 2 = -  log 2³ { Since, log 1 = 0}

⇒ n log 2 = - 3 log 2

⇒ n = - 3 (Answer)

Answer Link

Otras preguntas

A student added 5.350 g of ammonium chloride to 100.00 cm3 of water. the initial temperature of the water was 25.55℃ but it decreased to 21.79℃. calculate the e
When cell division is complete, compare the amount of chromosomes in each daughter cell to the original cell?
Why have ethnologists focused their study on "nonliterate" peoples?
help me with this question
what are physical activities for dance
Kevin turned the basketball over and over in his hand, feeling the roughness of the stitches, as he carefully placed the ball on his nightstand, he remembered t
PLEASE MATH HELP WILL GIVE BRAINLIEST What is the value of y?
The area of a square is 494949 square meters. how long is each side?
Show work!! What is the value of x? A.36 B.84 C.60 D.120
which action could be considered an effect of the protestant reformation