Mathematics Magazine for Grades 112 



3/2004 

I am not afraid of
tomorrow, for I have seen yesterday and I love today. Grade
12
Theory:
RULES OF LOGARITHMS 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: Log_{a }(uv) = Log_{a}(u) + Log_{a}(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 . Solution: 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 . Solution:
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: . Solution: If we have .
So
. 9 Evaluate the trigonometric limits: . Solution: It is known . We denote , if then
10 Calculate the limit: . Solution:
. We used and 
