Mathematics Magazine for Grades 1-12  




I am not afraid of tomorrow, for I have seen yesterday and I love today.
 - William Allen White

   Grade 12



Let a be a positive number such that a does not equal 1, let n be a real number, and let u and v be positive real numbers.

Logarithmic Rule 1: Loga (uv) = Loga(u) + Loga(v)

Logarithmic Rule 2:  

Logarithmic Rule 3:

Solutions from the Previous Issue: 

Proposed by Mihai Rosu Professor

1         Prove that the function    is a constant function

                        for every .


        Let us calculate value of function, we have:





2         Prove the identity.

Solution: We use the equality: and


3         Prove the identity .

Solution: We have successfully


Here we used the relation .


4         Prove that .




 Where we used , .


5         Prove that: .

Solution: We know that , then we have


6         Find    such as the expression   has a minim value.

Solution: Let A= .

A has a minimum if  is maximum, this is for  =1, thus  .


7         Solve the equation: .

Solution: We have  .

  So    .

8         Solve for x: . 


If      we have 


So  .

9         Evaluate the trigonometric limits: .

Solution: It is known  .

We denote , if   then

10      Calculate the limit: .



. We used and