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logarithm formula
The logarithm is indeed an exponential or power that must be applied to a base in order to achieve a particular number. Logarithms are represented mathematically as m is indeed the Logarithm of n towards the base b if bm = n, which may alternatively be written as m = logb n. For example,103 = 1000, then 3 = log101000
We also know that 103 = 1000, hence 3 = log101000. Common or Briggsian logarithms are sometimes referred to as common and Briggsian logarithms and are simply represented as log n.
Rules of Logarithms
There are seven Logarithm principles that are important for expanding, contracting, and solving Logarithmic equations. The following are the seven Logarithms rules:
1. Product Rule
Logb(P×Q) = logbp + logbQ
The product’s logarithm is equal to the sum of the components’ logarithms.
2. Rule of the Quotient
Logb(P/Q) = logbP − logbQ
The difference between the numerator and denominator logarithms is the logarithm of the ratio of two integers.
Basic Logarithm Formula
Some of the Different Basic Logarithm Formula are Given Below:
Examples
Example 1: a) 53 = 125 b) 3-3 = 1 / 27.
Solution:
Using the definition of the logarithm,
Bx = a ⇒ logbb a = x
Using this,
a) 53 = 125 ⇒ log5 125 = 3
b) 3-3 = 1 / 27 ⇒ log3 1/27 = -3
Answer: a) log5 125 = 3; b) log3 1/27 = -3.
Example 2: 5 log x + log y – 8 log z.
Solution:
To find: The compressed form of the given expression as a single logarithm using logarithm formulas.
5 log x + log y – 8 log z
= (5 log x – 8 log z) + log y (Regrouped the terms)
= (log x5 – log z8) + log y (∵ a log x = log xa)
= log (x5/z8) + log y (∵ log x – log y = log (x/y)
= log (x5y/z8) (∵ log x + log y = log (xy)
Answer: 5 log x + log y – 8 log z = log (x5y/z8).
Example 3: Find the integer value of log3 (1/9) using log formulas.
Solution:
Log3 (1/9) = log3 1 – log3 9 (∵ logb (x / y) = logb x – logb y)
= 0 – log3 32 (∵ logb 1 = 0)
= – 2 log3 3 (∵ logb ax = x logb a)
= -2 (1) (∵ logb b = 1)
= -2
Answer: log3 (1/9) = -2.
