Evaluate the logarithm. log base nine of quantity one divided by eighty one.

A logarithmic expression may be rewritten as an exponential expression: nine raised to the x-power equals one divided by eighty one: 9^x = 1/81. 1/18 is equal to 1/9^2, which is equal to 9^(-2). Now since nine raised to the x-power is equal to nine raised to the negative two power, x must be equal to negative two.