1.Characteristic of Logarithm.
a power m cross a power m equals a power m plus n in bracket ,a power m over a power n equals a power m minus n in bracket .Logarithm b to base a equals n, so equivalent with a power n equals b. For example:logarithm a to base g equals x,equivalent with g power x equals a,and logarithm b to base g equals y, equivalent with g power y equals b.
For example:
Logarithm a times b in bracket to base g equals …..
Problem Solving :
If:logarithm a to base g is x,so a equals g power x
logarithm b to base g ia y,so b equals g power y
with, a times b equals g power x times g power y , so equivalent with a times b equals g power x plus y in bracket.x plus y equals x plus y in bracket times logarithm g to base g,where logarithm g to base g equals 1, so logarithm a times b in bracket to base g equals x plus y.
So, for conclusion Logarithm a times b in bracket to base g equals logarithm a to base g plus logarithm b to base g.
a over b equals g power x over g over y ,equivalent a over b equals g over x minus y in bracket.Equivalent logarithm a over b to base g equals logarithm g power x minus y in bracket to base,and equivalent logarithm a over b to base g equals x minus y in bracket times logarithm g to base g,equivalent logarithm a over b to base g equals x minus y ,equivalent logarithm a over b in bracket to base g equals logarithm a to base g over logarithm b to base g.
For example:
Logarithm a to base g is x,so g power x equals a..........(1)
Logarithm b to base g is y,so g power y equals b………..(2)
Logarithm a power n to base g equals logarithm a times a times a times a…..times a,where a times a times a times a…..times a,counted n.And equivalent logarithm a power n to base g equals logarithm a to base g plus logarithm a to base g plus………..plus logarithm a to base g,and equivalent logarithm a power n to base g equals n times logarithm a to base g.
So,logarithm a power n to base g equals n times logarithm a to base g.
2.History of π (phi) number
Eigyp,used formula π times r squared for counting areas of circle,they used three point sixteen for value of π(phi),then in the mathematics in papyrus Rhind,value of π(phi) is three point sixteen.
But, now value of phi is three point fourteen. or same value with twenty two over seven.π(phi) used if we accounting areas or volume of cone , silinder ,circle ,act.
For example:We have circle with areas with one hundred fifty four, with radius seven.So,we can find phi with value three point fourteen.Areas of circle equals π times r square.It means π times seven squared equalsone hundred fifty four,With elaborate it ,so we can find value of π(phi) equals three point fourteen,or twenty two over seven.
3.History of formula ABC in square equals
for solution square equals we used formula often called formula ABC.This formula is minus b plus minus root of b square minus four times a times c in brackets all over two times a,it get from ax square times bx times c equals 0.then,this equals divided of a.and this equals have solution with prefect square.with solution equals formula ABC can find.
4.Proof square root of Irrational number.
Rasional number is fraction,or it can change with formula a over b, where a called numerator .and b called denominator. For example: five over four.ect,If square root of iirasional,so it can change in formula a over b. But in reality it can’t change in a over b.So,square root of two is irrational number.
5.y=x2+1 intersection with circle,where have radius root of 30.
