(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)

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)