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

Expand by moving outside the logarithm.

Apply the distributive property.

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.

Divide each term in by .

Simplify .

Dividing two negative values results in a positive value.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify each term.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Move the negative one from the denominator of .

Rewrite as .

Multiply by .

Move the negative in front of the fraction.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Solve for x 2^(3-x)=565