Problem solving

Shoptalk and explanations of how students use the English language:
I. The Nature of the logarithm.
We will discuss about the logarithm:
Remember from the exponential function:
A power of n to m times the power with the same power of n plus m in the bracket.
A power through the power of m to n with the same power mn minus the bracket.

Thus, the logarithm "b" with the basic number "of" the n → b the same with the power of n. logarithm "a" basis with the number "g" equals x → g with the same power of x. logarithm "b" with the bare "g" equals y → b equal to the power of g g. What you now, logarithm "a" time bracket?

Answer:
Assumed to:
Logarithm "a" basis with the number "g" equals x → g with the same power of x.
Logarithm "b" with the basic number "g" equals y → b equal to the power of g g.

A ↔ b times g is the same as the power of x times g to the power y

A ↔ b times g is the same as the power of x plus y in the bracket.

↔ logarithm "a" times "b" in the bracket with a base number "g" with the logarithm "g" to the power x plus y in the bracket base numbet with "g". Thus, the logarithm to the power of g in y plus x bracket to the base number "g" equals x plus y times the logarithm bracket "g" with the base number g equals x plus y.

↔ So, logarithm "a" times "b" in the bracket with a base number "g" with the same logarithm "a" basis with the number "g" loagrithm plus "b" with the basic number "g".

A ↔ b on the same power of x g to g to the power y. A b on the same power of g to x minus y in the bracket. Logarithm of b in the bracket over the base number "g". Logarithm of b in the bracket over the base number "g" equals x minus y times in the bracket g logarithm base number with "g". Logarithm of b in the bracket over the base number "g" equals x minus y. Thus, the logarithm of the b bracket base with the number "g" is the same as the minus logarithm base number "g" minus logarithm with base b number "g '.

II. abc Formula
We will discuss about abc Formula

We know that the square is the universal equations "a" times square plus x "b" times x plus "c" equal to zero. And then, if we want to square the difference between universal equality.
With all coeffisien with "a" and then we will piocure x square plus "b" above "that" time plus x "c" above "a" equal to zero. And then we internade plus for both the "b" on the open square bracket four times "a" close square bracket. So can equation is x square plus "b" above "the" square plus "b" on the open square bracket four times "a" close square bracket equal "b" on the open square bracket four times "a" close square bracket. We akan group to open bracket x plus two "a" bracket near the more than four square b "a" c minus b equals the square minus four times the square "a" times "c 'in the square bracket the whole time in the bracket. So , will be x plus "b" above two times open bracket "that" close bracket minus equals plus "b" minus four times the square "a" time bracket open bracket in the four "a" in the square bracket square root. So, we akan x equals minus b plus minus open bracket "b" minus four times the square "a" times "c" in the root square bracket bracket bracket close all open double "a". Thus, we can abc formula is x equals minus " b "open bracket plus minus" b "minus four times the square" a "times" c "in the square root bracket close all open twice close bracket.

III. Phy Number

A loop methode of measurement have been introduced by people in Egypt since 2450 BC with the triangle interralate. In Moscow papyrus rhind can be found and the task geometry. Where, the same sawed-circle with more than eight times nine diameters and volume of right cylinder with the height of the base times. Thus, we can irrespective of the circle is the same with more than eight times in nine diameters square bracket. We know that the same diameters radius twice, and then can find the same eight Ares circle with more than nine times in two times the radius of a square bracket equal to sixty-one eighty-four times more than four times the radius of a square with the two hundred and six more fivety of eighty times the radius of a square one with the three points six times the radius of a square. So, people in Egypt found that phy the first six three-point. Phy and analytical wisthel the same phy three point one four.

IV. Two square numbers is irrational.

Prove that the two-square number is irrational that we can issoscaller right triangle is the right one. Thus, we can determine apotema is one box plus one square root square bracket in the same two square root. We represent the two square root is a rational number meaning the number two square "a" top "b", where "a" and "b" is a prime number then the same two square root "of" more "b". "A" equal to twice the square root or b "a" square with two "b" square. Because "the" same square twice the integer "a" square of even integer. Prove "that" with the double "c" to the equations: four times the "c" the same square two times "b" square double "c" square equals "b" square. So, this proves that the two square root is irrational number.

V. Fine crossing y equals x minus one square a square and x plus y equals theerty square.

Our difference equations of x square plus y square theerty → y with the same square theerty minus x square.
plus y equals minus brecket open theerty minus x square bracket near the square root. We take y equals plus open bracket theerty minus x square bracket near the square root for y equals x square minus one in the first ans second quadrant.
We make x square minus one open bracket theerty near minus x square bracket square root. We place a square in the second. And x to the power of minus two times four square x minus one plus x theerty square. x to the power of minus three of the four-square minus x minus twenty-nine equal to zero.