# Solve for z 16^(2z+1)=8^(3-4z)

Create equivalent expressions in the equation that all have equal bases.
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
Solve for .
Simplify .
Apply the distributive property.
Multiply.
Multiply by .
Multiply by .
Simplify .
Apply the distributive property.
Multiply.
Multiply by .
Multiply by .
Move all terms containing to the left side of the equation.
Add to both sides of the equation.
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Subtract from .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Solve for z 16^(2z+1)=8^(3-4z)

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