Logarithms Rules logarithm all formulas 👇👇👇

 

Logarithms Rules 

logarithm all formulas 👇👇👇

1. Product Rule

logb(P×Q)=logbP+logbQ$${\mathrm{<span\; face=""Open\; Sans",\; sans-serif"\; style="background-color:\; white;\; font-size:\; 18px;\; text-align:\; justify;"> </span>}}_{}$$

The Logarithm of the product is the total of the Logarithm of the factors.

2. Quotient Rule

logb(PQ)=logbP−logbQ$${\mathrm{<br>}}_{}$$

 

The Logarithm of the ratio of two numbers is the difference between the Logarithm of the numerator and denominator. 

3. Power Rule

logb(PQ)=q×logbP

llogb(P×Q)=logbP+logbQ

The above property of the product rule states that the Logarithm of a positive number p to the power q is equivalent to the product of q and log of p.

4. Zero Rule  

logb(1)=0$${\mathrm{<br>}}_{}$$

 

The Logarithm of 1 such that b greater than 0 but b≠1, equals zero. 

5. The Logarithm of a Base to a Power Rule

logbby=y

 

The Logarithm of a base to a power rule states that the Logarithm of b with a rational exponent is equal to the exponent times its Logarithm.

6. A Base to a Logarithm Power Rule 

b^logy = y

 

The above rule states that raising the Logarithm of a number to the base of a Logarithm is equal to the number.

7. Identity Rule

logyy=1                    

• logb(m×n)=logbm+logbm$${\mathrm{<br>}}_{}$$
• logb(mn)=logbm−logbn$${\mathrm{<br>}}_{}$$
• logb(xy)=y×logbx$${\mathrm{<br>}}_{}$$

• logbn−−√m=logbn1m$${\mathrm{<br>}}_{}$$

• mlogb(x)+nlogb(y)=logb(xmyn)$$\mathrm{<br>}$$

 

Addition and Subtraction

• logb(m+n)=logbm+logb(1+nm)$${\mathrm{<br>}}_{}$$

• logb(m−n)=logbm+logb(1−nm)

by bhandari