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

Expand by moving outside the logarithm.

Rewrite as .

The natural logarithm of is .

Subtract from .

Move to the left of .

Rewrite as .

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 .

Move the negative in front of the fraction.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Solve for x (1/4)^x=75