Current Affairs 8th Class

Category : 8th Class

LOGARITHMS

FUNDAMENTALS

• Logarithm:- Let a be a positive real number other than 1 and \[{{a}^{x}}=m\], then x is called the logarithm of into the base and written as \[{{\log }_{a}}m\].

Example 1:- \[{{10}^{4}}=10000\]

\[\Rightarrow \text{lo}{{\text{g}}_{10}}10000=4\]

Example 2:- If \[{{3}^{-3}}=\frac{1}{27}\]

\[\Rightarrow {{\log }_{3}}\frac{1}{27}=-3\]

• \[(I)\,\,\text{lo}{{\text{g}}_{a}}(mn)={{\log }_{a}}m+\text{lo}{{\text{g}}_{a}}n\]
• \[(II)\,\,\text{lo}{{\text{g}}_{a}}\frac{m}{n}=\text{lo}{{\text{g}}_{a}}m-\text{lo}{{\text{g}}_{a}}n\]
• \[(III)\,\,{{\log }_{a}}a=1\]
• \[(IV)\,\,{{\log }_{a}}1=0\]
• \[(V)\,\,\text{lo}{{\text{g}}_{a}}m\,({{m}^{p}})=p(\text{lo}{{\text{g}}_{a}}m)\]
• \[(VI)\,\,\text{lo}{{\text{g}}_{a}}m=\frac{1}{{{\log }_{m}}a}\]
• \[(VII)\,\text{lo}{{\text{g}}_{a}}m=\frac{{{\log }_{b}}m}{{{\log }_{b}}a}=\frac{\log m}{\log a}\]