# Solve for y (1/4)^y=8^(y-1) (14)y=8y-1
Apply the product rule to 14.
1y4y=8y-1
One to any power is one.
14y=8y-1
Move 4y to the numerator using the negative exponent rule 1b-n=bn.
4-y=8y-1
Create equivalent expressions in the equation that all have equal bases.
22(-y)=23(y-1)
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
2(-y)=3(y-1)
Solve for y.
Multiply -1 by 2.
-2y=3(y-1)
Simplify 3(y-1).
Apply the distributive property.
-2y=3y+3⋅-1
Multiply 3 by -1.
-2y=3y-3
-2y=3y-3
Move all terms containing y to the left side of the equation.
Subtract 3y from both sides of the equation.
-2y-3y=-3
Subtract 3y from -2y.
-5y=-3
-5y=-3
Divide each term by -5 and simplify.
Divide each term in -5y=-3 by -5.
-5y-5=-3-5
Cancel the common factor of -5.
Cancel the common factor.
-5y-5=-3-5
Divide y by 1.
y=-3-5
y=-3-5
Dividing two negative values results in a positive value.
y=35
y=35
y=35
The result can be shown in multiple forms.
Exact Form:
y=35
Decimal Form:
y=0.6
Solve for y (1/4)^y=8^(y-1)

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