Laws of Logarithms

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1. \( \scriptsize log_aMN = log_aM+ log_aN \\ \ \scriptsize \rightarrow a^x \; \times \; a^y = a^x + a^y \)

2. \( \scriptsize log_a \left (\normalsize \frac {M}{N} \right) \scriptsize = log_a M \; – \; log_a N \\ \ \scriptsize → a^x \div a^y = a^{x-y}\)

3. \( \scriptsize log_a (M^n) = nlog_aM \\ \ \scriptsize→(a^x)^y = a^{xy}\)

(for any base “a” > 0, where a 1)

Note that the three basic laws of logarithms are closely related to those of indices given earlier on.
Note that \( \frac{logM}{logN} \neq \scriptsize log M \; – \; log N \)

Special Logarithms

4. log_aa = 1 → \( \scriptsize a^1 = a \)

5. log_a1 = 0 → \( \scriptsize a^0 \)

6. \( \scriptsize log_a \left ( \normalsize \frac{1}{a} \right) = \scriptsize -1 \rightarrow a^{-1} = \frac{1}{a} \)

7. \(\scriptsize log_a \left ( \normalsize \frac {1}{x} \right) \scriptsize = -log_a x \)

SS2: MATHEMATICS - 1ST TERM