5y+1-5y=8 fory

Move 8 to the left side of the equation by subtracting it from both sides.

5y+1-5y-8=0

Factor out 5y from the expression.

5y(5-1)

Add 8 to both sides of the equation.

5y+1-5y=8

Subtract 1 from 5.

5y⋅4=8

Move 4 to the left of 5y.

4⋅5y=8

Divide each term in 4⋅5y=8 by 4.

4⋅5y4=84

Cancel the common factor of 4.

Cancel the common factor.

4⋅5y4=84

Divide 5y by 1.

5y=84

5y=84

Divide 8 by 4.

5y=2

5y=2

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

ln(5y)=ln(2)

Use logarithm rules to move y out of the exponent.

yln(5)=ln(2)

Divide each term in yln(5)=ln(2) by ln(5).

yln(5)ln(5)=ln(2)ln(5)

Cancel the common factor of ln(5).

Cancel the common factor.

yln(5)ln(5)=ln(2)ln(5)

Divide y by 1.

y=ln(2)ln(5)

y=ln(2)ln(5)

y=ln(2)ln(5)

The result can be shown in multiple forms.

Exact Form:

y=ln(2)ln(5)

Decimal Form:

y=0.43067655…

Solve for y 5^(y+1)-5^y=8 fory