A. The Natures of Logarithm
a to the power of m times a to the power of n is equals to a to the power of m plus n in bracket. a to the power of m over a to the power of n is equals to a to the power of m minus n in bracket. Logarithm base a of b is equals to n, means that b is equals to a to the power of n. logarithm base g of a is equals to x, means that a is equals to g to the power of x. Logarithm base g of b is equals to y, means that b is equals to g to the power of y.
Logarithm base g of a times b in bracket is equals to? Let the logarithm base g of a is equals to x, so a is equals to g to the power of x. Logarithm base g of b is equals to y, so b is equals to g to the power of y. a times b is equals to g to the power of x times g to the power of y. a times b is equals to g to the power of x plus y in bracket. Logarithm base g of a times b in bracket is equals to logarithm base g of g to the power of x plus y in bracket. Its equals to x plus y in bracket times logarithm base g of g. We know that logarithm base g of g is equals to one. So the solution for logarithm base g of a times b in bracket is equals to x plus y.
Logarithm base g of a times b in bracket is equals to logarithm base g of a plus logarithm base g of b.
The Nature a.
Let the logarithm base g of a is equals to x, so a is equals to g to the power of x (equation I). Logarithm base g of b is equals to y, so b is equals to g to the power of y.
a over b is equals to g to the power of x over g to the power of y. Equals to a over b is equals to g to the power of x minus y in bracket. Logarithm base g of a over b is equals to logarithm base g of g to the power of x minus y in bracket. Equals to logarithm base g of a over b in bracket is equals to x minus y in braxket times logarithm base g of g. Logarithm base g of a over b in bracket is equals to x minus y in bracket, because logarithm base g of g is equals to one. So the conclusion is logarithm base g of a over b in bracket is equals to logarithm base g of a minus logarithm base g of b.


The Nature b.
Logarithm base g of a to the power of n is equals to logarithm base g of a times a times a times a times a times a times a until n times of a for each is a in bracket. Equals to logarithm base g of a plus logarithm base g of a plus logarithm base g of a plus logarithm base g of a until n quantifying tribes for each is logarithm base g of a. Equals to n times logarithm base g of a. So the logarithm base g of a to the power of n is equals to n times logarithm base g of a.
B. How To Find an Abc Formula
How to find an abc formula? First we know that the general equation of quadratic equation is a times x plus b times y plus c is equals to zero. And then from that formula we can dividing by a, so we will find other construction of quadratic equation. Then we will find new equation that is x plus b over a plus c over a is equals to zero. And then we used a completed square formula. We will found the quadratic form so we can find the x1 and x2. And finally we will find that x1,2 is equals to negative b plus minus square root of D all over by two times a. Which D is equals to b square minus 4 times a times c.
C. How To Find Phi Number
Phi number which we know is looking for by comparing the diameter and the circumference of circle. If we want to prove that, first we cut a string which has length of 22 cm, then we make it to the circle. We will get the diameter of the circle is 7 cm. from that experiment the phi number found.
D. The Square Root of 2 is Irrational Number
We know that hypotenuse of triangle (c) is the square root of quadrate of the two sides of triangle. When the triangle is right triangle with the same long of the side that is one, the long of the hypotenuse is square root of two. To prove the square root of two is irrational number we can used reduction ad absurdum or prove by contradiction. First we assumed that square root of two is rational number which has the form of m over n for m is integer number and n not both even. Then m square is equals to two times n square in bracket. Let m is two times p, so m is equals to 2 times n square, so 2 times p square is equals to n square, when n is also even. The contradiction is square root of two is irrational numbers.