Question

What is the solution to the exponential equation 1/64= 2^x+1

Answer 1

x = - 7

Explanation:

We have to get the solution to the exponential equation
`(1)/(64) = 2^((x + 1))`.

Now,
`(1)/(64) = 2^((x + 1))`

⇒
`(1)/(2^(6)) = 2^((x + 1))`

⇒
`2^(- 6) = 2^((x + 1))`

{Since we know the properties of exponent as
`a^(- b) = (1)/(a^(b) )` }

⇒ - 6 = (x + 1)

{Since the base are same i.e. 2 so, we can equate the power terms of both sides}

⇒ x = - 6 - 1 = - 7 (Answer)