Fundamental equations:

            [H₃O⁺][OH¯]  =  K_w  =  1.0 x 10^-14           pX  =  -logX             K_aK_b  =  K_w

All the ways you can find [H₃O⁺] and [OH¯]:

All the ways you can find pH and pOH:

            pH  +  pOH  =  14       pH  =  14 – pOH         pOH  =  14 – pH

            pH  =  -log[[H₃O⁺]                                           pOH  =  -log[OH¯]

K_aK_b = K_w  is used in hydrolysis problems.  Use it to calculate the K_b of the conjugate base of a weak acid, or conversely, the K_a of the conjugate acid of a weak base:

In general, pX is a power function, and it means you take the negative logarithm of the variable or number, hence, pX  =  -logX.