Answer:
x = - 7
Step-by-step explanation:
We have to get the solution to the exponential equation [tex]\frac{1}{64} = 2^{(x + 1)}[/tex].
Now, [tex]\frac{1}{64} = 2^{(x + 1)}[/tex]
⇒ [tex]\frac{1}{2^{6}} = 2^{(x + 1)}[/tex]
⇒ [tex]2^{- 6} = 2^{(x + 1)}[/tex]
{Since we know the properties of exponent as [tex]a^{- b} = \frac{1}{a^{b} }[/tex] }
⇒ - 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)
