${{\log }_{a}}b+{{\log }_{a}}c={{\log }_{a}}\left( b\times c \right)$ 








e.g. $\ln 2+ln5=ln10$ , ${{\log }_{3}}2+{{\log }_{3}}20={{\log }_{3}}40$, 
${{\log }_{2}}3+{{\log }_{2}}7+{{\log }_{2}}2={{\log }_{2}}42$
Important notes:
${{\log }_{a}}(p+q)\ne \left( lo{{g}_{a}}p \right)\left( lo{{g}_{a}}q \right)$ 
${{\log }_{a}}(p+q)\ne lo{{g}_{a}}p+lo{{g}_{a}}q$

${{\log }_{a}}b+{{\log }_{a}}c={{\log }_{a}}\left( b\times c \right)$ 









e.g. $\ln 2+ln5=ln10$ , ${{\log }_{3}}2+{{\log }_{3}}20={{\log }_{3}}40$, 

${{\log }_{2}}3+{{\log }_{2}}7+{{\log }_{2}}2={{\log }_{2}}42$

${{\log }_{a}}(p+q)\ne \left( lo{{g}_{a}}p \right)\left( lo{{g}_{a}}q \right)$ 

${{\log }_{a}}(p+q)\ne lo{{g}_{a}}p+lo{{g}_{a}}q$

Product Law

Product Law