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)

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)