I. The Nature of Logarithm.
Remember of Exponent function :
A to the power of m times a to the power of n equals a to the power of m plus n in bracket.
A to the power of m over a to the power of n equals a to the power of m minus n in bracket.
So, logarithm “b” with a base number “a” equals n →b equals a to the power of n. logarithm “a” with a base number “g” equals x →a equals g to the power of x. logarithm “b” with a bare number “g” equals y →b equals g to the power of g. What do you now, logarithm “a” times in bracket ?
Answer :
To assumed :
Logarithm “a” with a base number “g” equals x→a equals g to the power of x.
Logarithm “b” with base number “g” equals y→b equals g to the power of g.
↔ A times b equals g to the power of x times g to the power of y
↔ A times b equals g to the power of x plus y in bracket.
↔ Logarithm “a” times “b” in bracket with a base number “g” equals logarithm “g” to the power of x plus y in bracket with a base numbet “g”. So, logarithm g to the power of x plus y in bracket with a base number “g” equals x plus y in bracket times logarithm “g” with a base number g equals x plus y.
↔ So, logarithm “a” times “b” in bracket with a base number “g” equals logarithm “a” with a base number “g” plus loagrithm “b” with a base number “g”.
↔ A over b equals g to the power of x over g to the power of y. A over b equals g to the power x minus y in bracket. Logarithm a over b in bracket with a base number “g”. Logarithm a over b in bracket with a base number “g” equals x minus y in bracket times logarithm g with a base number “g”. Logarithm a over b in bracket with a base number “g” equals x minus y. So, logarithm a over b in bracket with a base number “g” minus equals logarithm with a base number “g” minus logarithm b with a base number “g’.
II. abc Formula
We know that square equations of universal is “a” times x square plus “b” times x plus “c” equals zero. And then, if we want to difference square equation of universal.
With all over coeffisien with “a” and then we will piocure x square plus “b’ over “a” times x plus “c’ over “a” equals zero. And then we are plus to second internade with “b” square over open bracket four times “a” square close bracket. So be can equation is x square plus “b” over “a” square plus “b” square over open bracket four times “a” square close bracket equals “b” square over open bracket four times “a” square close bracket. We will a group to x plus open bracket two “a” close bracket equals b square over four “a” square minus c over a equals b square minus four times “a” times “c’ in bracket all over four times a square in bracket. So, be can x plus “b” over open bracket two times “a” close bracket equals plus minus “b” square minus four times “a” times in bracket all over open bracket four times “a” square in bracket square root. So, we will x equals minus b plus minus open bracket “b” square minus four times “a” times “c” in bracket square root close bracket all over open bracket two times “a”. So, we can abc formula is x equals minus “b” plus minus open bracket “b” square minus four times “a” times “c” in bracket square root close bracket all over open bracket two times a close bracket.
III. Phy Number
A circle measurement methode has introduced by people in Egypt since 2450 SM with interralate triangle. In papyrus moskow and rhind can found task of geometry. Where, area of circle sawed equals eight over nine time diameters and then volume of cylinders right equals area of base times height. So, we can apart is area of circle equals eight over nine times diameters in bracket square. We know that diameters equals two times radius, and then can found the ares of circle equals eight over nine times two times radius in bracket square equals sixty four over eighty one times four times radius square equals two hundred fivety six over eighty one times radius square equals three point one six times radius square. So, people in Egypt has found phy number is three point one six. And then phy analytic wisthel that phy equals three point one four.
IV. Two square is irrational number.
Remember of Exponent function :
A to the power of m times a to the power of n equals a to the power of m plus n in bracket.
A to the power of m over a to the power of n equals a to the power of m minus n in bracket.
So, logarithm “b” with a base number “a” equals n →b equals a to the power of n. logarithm “a” with a base number “g” equals x →a equals g to the power of x. logarithm “b” with a bare number “g” equals y →b equals g to the power of g. What do you now, logarithm “a” times in bracket ?
Answer :
To assumed :
Logarithm “a” with a base number “g” equals x→a equals g to the power of x.
Logarithm “b” with base number “g” equals y→b equals g to the power of g.
↔ A times b equals g to the power of x times g to the power of y
↔ A times b equals g to the power of x plus y in bracket.
↔ Logarithm “a” times “b” in bracket with a base number “g” equals logarithm “g” to the power of x plus y in bracket with a base numbet “g”. So, logarithm g to the power of x plus y in bracket with a base number “g” equals x plus y in bracket times logarithm “g” with a base number g equals x plus y.
↔ So, logarithm “a” times “b” in bracket with a base number “g” equals logarithm “a” with a base number “g” plus loagrithm “b” with a base number “g”.
↔ A over b equals g to the power of x over g to the power of y. A over b equals g to the power x minus y in bracket. Logarithm a over b in bracket with a base number “g”. Logarithm a over b in bracket with a base number “g” equals x minus y in bracket times logarithm g with a base number “g”. Logarithm a over b in bracket with a base number “g” equals x minus y. So, logarithm a over b in bracket with a base number “g” minus equals logarithm with a base number “g” minus logarithm b with a base number “g’.
II. abc Formula
We know that square equations of universal is “a” times x square plus “b” times x plus “c” equals zero. And then, if we want to difference square equation of universal.
With all over coeffisien with “a” and then we will piocure x square plus “b’ over “a” times x plus “c’ over “a” equals zero. And then we are plus to second internade with “b” square over open bracket four times “a” square close bracket. So be can equation is x square plus “b” over “a” square plus “b” square over open bracket four times “a” square close bracket equals “b” square over open bracket four times “a” square close bracket. We will a group to x plus open bracket two “a” close bracket equals b square over four “a” square minus c over a equals b square minus four times “a” times “c’ in bracket all over four times a square in bracket. So, be can x plus “b” over open bracket two times “a” close bracket equals plus minus “b” square minus four times “a” times in bracket all over open bracket four times “a” square in bracket square root. So, we will x equals minus b plus minus open bracket “b” square minus four times “a” times “c” in bracket square root close bracket all over open bracket two times “a”. So, we can abc formula is x equals minus “b” plus minus open bracket “b” square minus four times “a” times “c” in bracket square root close bracket all over open bracket two times a close bracket.
III. Phy Number
A circle measurement methode has introduced by people in Egypt since 2450 SM with interralate triangle. In papyrus moskow and rhind can found task of geometry. Where, area of circle sawed equals eight over nine time diameters and then volume of cylinders right equals area of base times height. So, we can apart is area of circle equals eight over nine times diameters in bracket square. We know that diameters equals two times radius, and then can found the ares of circle equals eight over nine times two times radius in bracket square equals sixty four over eighty one times four times radius square equals two hundred fivety six over eighty one times radius square equals three point one six times radius square. So, people in Egypt has found phy number is three point one six. And then phy analytic wisthel that phy equals three point one four.
IV. Two square is irrational number.
Prove that two square is irrational number is we can a issoscaller right triangle with right side is one. So, we can determine apotema is one square plus one square in bracket square root equals two square root. We represent two square root is rational number the meaning of two square number equals “a” over “b”, where “a” and “b” is a integer prime then two square root equals “a” over “b”. “a” equals b times two square root or “a” square equals two times “b” square. Because “a” square equals two times a integer then “a” square of even integer. Prove “a” equals two times “c” then equations to: four times “c” square equals two times “b” square two times “c” square equals “b” square. So, that is prove of two square root is a irrational number.
V. Fine Intersection of y equals x square minus one and x square plus y square equals theerty.
We difference equations of x square plus y square equals theerty →y square equals theerty minus x square.
y equals plus minus open brecket theerty minus x square close bracket square root. We take y equals plus open bracket theerty minus x square close bracket square root because y equals x square minus one in first ans second quadrant.
We make x square minus one equals open bracket theerty minus x square close bracket square root. We square in second space. Then x to the power of four minus two times x square plus one equals theerty minus x square. x to the power of four minus three minus x square minus twenty nine equals zero.
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