The logarithmic expression is . \ \

Find the expression. \ \

Case (i): \ \

                (First expression) \ \

          (Let the logarithm equal ) \ \

                  (Logarithm formula: if and only if ) \ \

                  (Substitute: ) \ \

Equality for exponential functions property: if and only if . \ \

. \ \

           (Substitute ) \ \

Case (ii): \ \

                (Second expression) \ \

          (Let the logarithm equal ) \ \

                  (Logarithm formula: if and only if ) \ \

                  (Substitute: and ) \ \

Equality for exponential functions property: if and only if . \ \

. \ \

                    (Simplify) \ \

        (Substitute ) \ \

Case (iii): \ \

                (Three expression) \ \

         (Let the logarithm equal ) \ \

                (Logarithm formula: if and only if ) \ \

Equality for exponential functions property: if and only if . \ \

. \ \

        (Substitute ) \ \

Case (iv): \ \

                  (Four expression) \ \

            (Let the logarithm equal ) \ \

                   (Logarithm formula: if and only if ) \ \

                    (Substitute: and ) \ \

Equality for exponential functions property: if and only if . \ \

. \ \

                     (Simplify) \ \

        (Substitute ) \ \

Case (v):

                (Fifth expression) \ \

          (Let the logarithm equal ) \ \

                (Logarithm formula: if and only if ) \ \

                    (Substitute: and ) \ \

Equality for exponential functions property: if and only if . \ \

. \ \

                        (Simplify) \ \

        (Substitute ) \ \

Since add all cases of the expression to find the original expression value. \ \

\ \

            (Substitute , , , and ) \ \

      (LCM is ) \ \

                                     (Add) \ \

                                     (Simplify) \ \

. \ \

Simplified value of the expression is .