Properties of logarithms

Introduction:

We use logarithms to mark terms linking various forms of powers in a different form. If you can job self-assuredly with powers in dissimilar analysis you should have no problems conduct logarithms.

mmediately as calculation is the opposite process of addition, and taking a square root is the opposite action of squaring, exponentiation logarithms are inverse operations. Decision an antilog is the opposite operation of judgment a log, so is an additional name for exponentiation.

Three Properties of Logarithms

Following are the three properties of Logarithms.

Multiplication property:

The first property of logarithms is declare what is the rule when you multiply two values with the same base together

(x² * x³) Recall that logarithm is exponents, and when you multiply, you are going to add the logarithms.

log_c xy = log_c x + log_c y.

Example problem:

1. Log₅50

Log₅(25 * 2 )= log₅ 25+log₅ 2

2. Log₅ 80

Log₅(40 * 2 )= log₅ 40+log₅ 2.

Division property:

The second property of logarithms are the law what time you divide two values by resources of the similar base is the way to subtract the exponents. Therefore, the law for division is the method to subtract the logarithms.

The log of a calculate is the dissimilarity of the logs.

Log_c (x/y) = log_c x – log_c y.

Example problem:

1) Log₅ 60

Log₅(20/3) = log₅ 20- log₅ 3

2). Log₅ 120

Log₅(60/2) = log₅ 60 – log₅ 2

Raising to a Power property:

The third property of logarithms are what time you increase a quantity to a power, the law is that you multiply the exponents jointly. In logarithms properties the exponent scheduled the argument is the coefficient of the log.

log_c x^r = r * log_c x.

Example problem:

Log₅100²=2 log₅100

= 2 log₅(10*10)

= 2 (log₅10 + log₅10)

= 2(2 log₅10)

Log₅100²= 4 log₅10