swagger1035
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  • 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)

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