# Evaluate 9^(2x)*0.27^(3-x)=1/9

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Expand the left side.
Rewrite as .
Expand by moving outside the logarithm.
Expand by moving outside the logarithm.
Apply the distributive property.
Move .
Move all the terms containing a logarithm to the left side of the equation.
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Add to both sides of the equation.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify .
Move the negative in front of the fraction.
Simplify terms.
Combine the numerators over the common denominator.
Factor out of .
Factor out of .
Factor out of .
Simplify the expression.
Rewrite as .
Move the negative in front of the fraction.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Evaluate 9^(2x)*0.27^(3-x)=1/9

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