Thus, the fact that 100 = 102 says that 2 is the logarith of 100 to the base 10. It is written as 2=10log100 0r 10log100=2. But, it can be read : logarithm of 100 to the base 10 equals 2.
Characteristic of logarithm
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 by a to the power of n equals a to the power of m minus n in bracket.
Logarithm of b to the base a equals n equivalent with b equals a to the power of n.
Logarithm of a to the base g equals x. So, a equals g to the power of x.
Logarithm of b to the base g equals y. So, b equals g to the power of y.
Logarithm of a to the power of n to the base g equals n times logarithm of a to the base g.
We will find the solving of logarithm of a times b in bracket to the base g. [glog(axb=..?]
Let, Logarithm of a to the base g equals x. So, a equals g to the power of x.
Logarithm of b to the base g equals y. So, b equals g to the power of y.
From two character of logarithm above, is got that a times b equals g to the power of x times g to the power of y.
g to the power of x times g to the power of y equivalent g to he power of x plus y in bracket.
So, a times b equals g to he power of x plus y in bracket.
We can conclude that logarithm of a times b in bracket to the base g equals logarithm of a to the base g plus logarithm of b to the base g.
In this section, we will prove that square root of two is irrational number.
Let, square root of two is irrational number, it means that square root of two equals a over b, where a and b as prim number.
square root of two equals a over b. So, a equals square root of two times b or a square equals two times b square.
From this solving, we get that b square is even number and b is also even number. But, this is impossible because the prim number is relative. So, the assumption that square root of two have rational characteristic is impossible and must be delayed.
How was the value of phi is invented
The ancient Egyptian had invented the phi value is 3,16 (three point one six). They found it by assumpt that the circle area equals eight ninth times diametre (d) in bracket square.
We know that d equals two times radius. So, we can get the circle area equals eight ninth times two times radius (r) in bracket square. It is equivalent sixty four over by eighty one times four times r square. It is equals two hundred and fifty sixty over eighty one times r square.
So, the circle area is three point one six times r square. we know that the circle area is phi times radius square. we can find that the value of phi is three point one six.
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