Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

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.

Subtract from both sides of the equation.

Add to both sides of the equation.

Factor out of .

Factor out of .

Factor out of .

Rewrite as .

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