Answer:
x = -7
Step-by-step explanation:
This is an exponential equation.
[tex]\frac{1}{2}^x=128[/tex]
We need to take log(or ln) of both sides and use logarithm property to solve this.
So, let's take ln of both sides, so we have:
[tex]ln(\frac{1}{2}^x)=ln(128)[/tex]
Now, we will use this property shown below to further simplify:
[tex]ln(a^b)=bln(a)[/tex]
So, we now have:
[tex]ln(\frac{1}{2}^x)=ln(128)\\xln(\frac{1}{2})=ln(128)\\x=\frac{ln(128)}{ln(\frac{1}{2})}\\x=-7[/tex]
The value of x is -7
