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(1/2)^x=16^2

Could you please help me with the step-by step? This problem is giving me trouble. ​

(1/2)^x=16^2 Could you please help me with the step-by step? This problem is giving-example-1
User Asmoun
by
6.8k points

1 Answer

6 votes

Write both sides as powers of 2. First,

1/2 = 2⁻¹

16 = 2⁴

so the equation can be rewritten as

(1/2)ˣ = 16²

(2⁻¹)ˣ = (2⁴)²

Recall that
(a^b)^c=a^(bc), so that

2⁻ˣ = 2⁸

The bases are the same, so the exponents must be equal:

-x = 8

x = -8

User ARobertson
by
6.5k points
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