Lesson An overview to the laws of logarithms

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very first---the logarithm of a number n is the the exponent of 10 where 10 should be raised to obtain b. EXAMPLE---log%28100%29=2 because 10%5E2=100

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

logarithm of a product:
log+%28xy%29=log+%28x%29+%2B+log%28y%29
logarithm of a quotient:
log%28x%2Fy%29=log%28x%29-log%28y%29
This are the Foundations of the this law: logarithm of powers
x%5En is defined as x multiplied n times to itself.

Thus,
log%28x%5En%29=n+log%28x%29
This is similar to the logarithm of roots.
Remember that roots can be expressed as fractional exponents.
So, square root of x=x%5E%281%2F2%29, cube root of x=x%5E%281%2F3%29 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%281%2Fx%29=0-log+%28x%29
________=-+log%28x%29
And, in modern math, negative logarithms are called COLOGARITHMS!
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