Logarithms–Important Laws & Formulas

Q) Why log 1=0?

The important thing to remember is the log represents the exponent.  In the case of common logs, the base is always base 10.  Now lets see some examples which clears your doubt:

1) log 100 = 2 because 10² = 100.
2) log 1000 = 3 because 10³ = 1000.
3) log 1 = 0 because 10⁰ = 1.
4)  log .1 = -1 because 10^-1 = .1
5)  log .01 = -2 because 10^-2 = .01
Q) How to change base in logarithms?
We can change any base to a different base any time we want. The most used bases are obviously base 10 and base e.
Change of base formula:  Log_b x = Log_a x/Log_a b

Q) Some Important Laws/Formulas in Logarithms:
1)  Log_b MN = Log_b M + Log_b N
2)  Log_b M/N = Log_b M - Log_b N
3)  Log_b M = Log_b N if and only if M = N
4)  Log_b M^k = k Log_b M
5)  Log_b b = 1
6)  Log_b 1 = 0
7)  Log_b b^k = k
8) _bLog_b x _{= x}

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