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
- log2 3(4) =log2 3 + log2 4
- log7 5(6) =log7 5 + log7 6
- log15 8(12) =log15 8 + log15 12
- log11 9(7) =log11 9 + log11 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
- log2 5/6 =log2 5 - log2 6
- log3 7/8 =log3 7 - log3 8
- log5 3/4 =log5 3 - log5 4
- log7 6/11 =log7 6 - log7 11
Law 3: The logarithm of x with a rational exponent is equal to the exponent times the logarithm.
log b xn = n log b x
- log2 56 =6 log2 5
- log3 78 =8 log3 7
- log5 123 =3 log5 12
- log9 97 =7 log9 9
- log3 71/4 =1/4 log3 7
- log9 97/3 =7/3 log9 9