Many standardized tests will challenge you with these three laws of logarithms.

Law 1: The logarithm of a product is equal to the sum of the logarithms of each term in the product.

*log _{b} xy = log _{b} x + log _{b} y*

- log
_{2}*3(4)*=log_{2}*3*+ log_{2}*4* - log
_{7}*5(6)*=log_{7}*5*+ log_{7}*6* - log
_{15}*8(12)*=log_{15}*8*+ log_{15}*12* - log
_{11}*9(7)*=log_{11}*9*+ log_{11}*7*

Law 2: The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator.

*log _{b} ^{x}/_{y} = log _{b} x – log _{b} y*

- log
_{2}=^{5}/_{6}log_{2}*5*- log_{2}*6* - log
_{3}=^{7}/_{8}log_{3}*7*- log_{3}*8* - log
_{5}=^{3}/_{4}log_{5}*3*- log_{5}*4* - log
_{7}=^{6}/_{11}log_{7}*6*- log_{7}*11*

Law 3: The logarithm of *x* with a rational exponent is equal to the exponent times the logarithm.

*log _{b} x^{n} = n log _{b} x *

- log
_{2}*5*=^{6}6 log_{2}*5* - log
_{3}*7*=^{8}8 log_{3}*7* - log
_{5}*12*=^{3}3 log_{5}*12* - log
_{9}*9*=^{7}7 log_{9}*9* - log
_{3}*7*=^{1/4}^{1}/_{4}log_{3}*7* - log
_{9}*9*=^{7/3}^{7}/_{3}log_{9}*9*