**1. if n and a are positive real numbers, and a is not equal to 1, then**

If ax = n, then log a n = x

**2. log a n is called logarithmic function. The domain of logarithmic function is positive real numbers and the range is all real numbers.**

**3. log of 1 to any base is 0**

log b 1 = 0

**4. log of any number to base as itself is 1,**

log a a = 1

**5. Logarithm of a Product**

log a pq = log a p + loga q

**6. Logarithm of a Fraction**

log a (p/q) = log a p – log a q

**7. log a pn = n log a p**

**8. a(log a p) = p**

**9. Base Change Rule of Logarithms:**

log a n = log b n × log a b

**10. log a b = (log nb)/(log n a)**

**11. if the base is 10, then**

log a b = (log b)/(log a)

**12. (log a b) × (log b a ) = 1**

**13. log a b = 1/log b a**

**14. log (m + n ) is not equal to log m + log n**

**15. log an p = 1/n (log a p)**

**16. log an bm = (m/n)log a b**

**17. log 10 b is called common logarithm because the base is 10**

**18. log e b is called natural logarithm. It is denoted by ln b.**

**19. log 1/a b = -log a b**

**20. log a (1/b) = -log a b**

**21. log 1/a (1/b) = log a b**