Lesson An overview to the laws of logarithms

very first---the logarithm of a number n is the the exponent of 10 where 10 should be raised to obtain b. EXAMPLE--- log(100)=2

because

First I will tackle the most basic laws: the logarithm of a product and the logarithm of a quotient.

logarithm of a product:
log (xy)=log (x) + log(y)

logarithm of a quotient:
log(x/y)=log(x)-log(y)

This are the Foundations of the this law: logarithm of powers
x^n

is defined as x multiplied n times to itself.

Thus,
log(x^n)=n log(x)

This is similar to the logarithm of roots.
Remember that roots can be expressed as fractional exponents.
So, square root of x= x^(1/2)

, cube root of x= x^(1/3)

and so on.
Thus,
log(x^(1/n))=(1/n) log (x).

Now let's recall this identity: log(1)=0
So, let us formulate the logarithm of reciprocals.
log(1/x)=0-log (x)

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And, in modern math, negative logarithms are called COLOGARITHMS!
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