If 2^x-1 + 2^x-2 + 2^x-3 = 1/16, find 2^x. Including a solution is greatly appreciated. Thank you :)
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If 2^x-1 + 2^x-2 + 2^x-3 = 1/16, find 2^x. Including a solution is greatly appreciated. Thank you :)
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Answer:
The result can be shown in multiple forms.
Exact Form:
x=5
—
2
Decimal Form:
x=2.5
Mixed Number Form:
x=2 1
—
2
Step-by-step explanation:
2^2x−1=16
Create equivalent expressions in the equation that all have equal bases.
2^2x–1=2⁴
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
2x−1=4
Solve for x
Move all terms not containing x to the right side of the equation.
Add 1 to both sides of the equation.
2x=4+1
Add 4 and 1.
2x=5
Divide each term by 2 and simplify.
Divide each term in 2x=5 by 2.
2x=5
— —
2 2
Cancel the common factor of 2.
Cancel the common factor.
2x=5
— —
2 2
Divide x by 1.
x=5
—
2
The result can be shown in multiple forms.
Exact Form:
x=5
—
2
Decimal Form:
x=2.5
Mixed Number Form:
x=2 1
—
2