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

Math
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 by 4 and simplify.
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Divide each term in 4⋅5y=8 by 4.
4⋅5y4=84
Cancel the common factor of 4.
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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 by ln(5) and simplify.
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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).
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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

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