# Solve for y 5^(y-4)=3^(2y) 5y-4=32y
Take the log of both sides of the equation.
ln(5y-4)=ln(32y)
Expand ln(5y-4) by moving y-4 outside the logarithm.
(y-4)ln(5)=ln(32y)
Expand ln(32y) by moving 2y outside the logarithm.
(y-4)ln(5)=2yln(3)
Solve the equation for y.
Apply the distributive property.
yln(5)-4ln(5)=2yln(3)
Subtract 2yln(3) from both sides of the equation.
yln(5)-4ln(5)-2yln(3)=0
Add 4ln(5) to both sides of the equation.
yln(5)-2yln(3)=4ln(5)
Factor y out of yln(5)-2yln(3).
Factor y out of yln(5).
y(ln(5))-2yln(3)=4ln(5)
Factor y out of -2yln(3).
y(ln(5))+y(-2ln(3))=4ln(5)
Factor y out of yln(5)+y(-2ln(3)).
y(ln(5)-2ln(3))=4ln(5)
y(ln(5)-2ln(3))=4ln(5)
Divide each term by ln(5)-2ln(3) and simplify.
Divide each term in y(ln(5)-2ln(3))=4ln(5) by ln(5)-2ln(3).
y(ln(5)-2ln(3))ln(5)-2ln(3)=4ln(5)ln(5)-2ln(3)
Cancel the common factor of ln(5)-2ln(3).
Cancel the common factor.
y(ln(5)-2ln(3))ln(5)-2ln(3)=4ln(5)ln(5)-2ln(3)
Divide y by 1.
y=4ln(5)ln(5)-2ln(3)
y=4ln(5)ln(5)-2ln(3)
y=4ln(5)ln(5)-2ln(3)
y=4ln(5)ln(5)-2ln(3)
The result can be shown in multiple forms.
Exact Form:
y=4ln(5)ln(5)-2ln(3)
Decimal Form:
y=-10.95253096…
Solve for y 5^(y-4)=3^(2y)

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