Given that 2 {}^(x) = 0.125 Find x ​

Question

Given that

`2 {}^(x) = 0.125`
Find x
​

Answer 1

x = -3.

Explanation:

2^x = 0.125

Taking logs:

x ln 2 = ln 0.125

x = ln 0.125 / ln 2

x = -3

Answer 2

Take the natural log of both sides

ln(2^x)=ln(.125)
Xln(2)=ln(.125)
X=ln(.125)/ln(2)
X=-3

ALTERNATIVE ROUTE:
You know that 0.125 is equal to 1/8
And 1/2^3 is also equal to 1/8
So since you need the reciprocal to match it the exponent is a negative