Logarithmic laws for the common logarithm

Summary

Logarithmic identities

• \(log {10}^a=a\) for all \(a\)
• \({10}^{log c}=c\) for \(c>0\)

Notation

• \(log cd\) means \(log \left( cd \right)\) . \(log c/d\) means \(log \left( c/d \right)\)
• \(log c+d\) means \(\left( log c \right)+d\) . To log a sum, write \(log \left( c+d \right)\)
• \(log a^b\) means \(log \left( a^b \right)\) . To take \(log a\) to the power \(b\) , write \({\left( log a \right)}^b\)

Logarithm of products, ratios and powers

• \(log cd=log c+log d\)
• \(log \frac{c}{d}=log c-log d\)
• \(log c^d=dlog c\)