# Solve for z 3^(4z+1)=9^(3z-5) 34z+1=93z-5
Create equivalent expressions in the equation that all have equal bases.
34z+1=32(3z-5)
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
4z+1=2(3z-5)
Solve for z.
Simplify 2(3z-5).
Apply the distributive property.
4z+1=2(3z)+2⋅-5
Multiply.
Multiply 3 by 2.
4z+1=6z+2⋅-5
Multiply 2 by -5.
4z+1=6z-10
4z+1=6z-10
4z+1=6z-10
Move all terms containing z to the left side of the equation.
Subtract 6z from both sides of the equation.
4z+1-6z=-10
Subtract 6z from 4z.
-2z+1=-10
-2z+1=-10
Move all terms not containing z to the right side of the equation.
Subtract 1 from both sides of the equation.
-2z=-10-1
Subtract 1 from -10.
-2z=-11
-2z=-11
Divide each term by -2 and simplify.
Divide each term in -2z=-11 by -2.
-2z-2=-11-2
Cancel the common factor of -2.
Cancel the common factor.
-2z-2=-11-2
Divide z by 1.
z=-11-2
z=-11-2
Dividing two negative values results in a positive value.
z=112
z=112
z=112
The result can be shown in multiple forms.
Exact Form:
z=112
Decimal Form:
z=5.5
Mixed Number Form:
z=512
Solve for z 3^(4z+1)=9^(3z-5)

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