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denis23 [38]
3 years ago
9

Given that

5" alt="2 {}^{x} = 0.125" align="absmiddle" class="latex-formula">
Find x
​
Mathematics
2 answers:
Luda [366]3 years ago
5 0
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
iris [78.8K]3 years ago
5 0

Answer:

x = -3.

Step-by-step explanation:

2^x = 0.125

Taking logs:

x ln 2 = ln 0.125

x = ln 0.125 / ln 2

x = -3

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