Mathematics Magazine for Grades 1-12
I am not afraid of
tomorrow, for I have seen yesterday and I love today.
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: 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 .
8 Solve for x: .
If we have
9 Evaluate the trigonometric limits: .
Solution: It is known .
We denote , if then
10 Calculate the limit: .
. We used and