## Pages

### Law of subtraction of logarithms:

log_m(a)-log_m(b)=log_m(a/b)
"When two logarithms (of the same base) are subtracted, the result is a logarithm of the quotient of the two logarithms"
Note: The above law applies to logarithms with same bases, not with different bases.

### Examples:

• log_10(40)-log_10(2)=log_10(50/2)=log_10(25)
• log_m(x)-log_m(y)=log_m(x/y)
• log(x^2y^2)-log(xy)=log((x^2y^2)/(xy))=log(xy)
• log(6x)-log(9x)=log((6x)/(9x))=log(1/3)

### Subtracting logarithms with different bases:

Logarithms with different bases can not be subtracted by the above mentioned law. However, by converting their bases to a common base, the logarithms can then be simplified as shown in the following example:
log_2(20)-log_3(30)=(log(2))/(log(20))-log(3)/log(30)
=  {log2 * log(30) - log(3) * log(20)}/{log(20) * log(30)}

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