Question

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

A. -3
B. -4
C. 3
D. 4​

Answer 1

n = - 3

Explanation:

We have to solve the equation
`2^(n) = (1)/(8)` for n.

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

So,
`2^(n) = (1)/(8)`

⇒
`\log 2^(n) = \log (1)/(8)`

⇒ n log 2 = log 1 - log 8 {Since we know the property of logarithm
`\log a^(b) = b \log a` and
`\log (a)/(b) = \log a - \log b`}

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

⇒ n log 2 = - 3 log 2

⇒ n = - 3 (Answer)