# 8th Class Mathematics Logarithms

Logarithms

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 ${{3}^{-3}}=\frac{1}{27}$

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

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

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