according to logarithm property log (a.b)=
Answers
Answer:
Throughout your study of algebra, you have come across many properties—such as the commutative, associative, and distributive properties. These properties help you take a complicated expression or equation and simplify it.
The same is true with logarithms. There are a number of properties that will help you simplify complex logarithmic expressions. Since logarithms are so closely related to exponential expressions, it is not surprising that the properties of logarithms are very similar to the properties of exponents. As a quick refresher, here are the exponent properties.
Properties of Exponents
Product of powers:
Quotient of powers:
Power of a power:
One important but basic property of logarithms is logb bx = x. This makes sense when you convert the statement to the equivalent exponential equation. The result? bx = bx.
Let’s find the value of y in. Remember , so means and y must be 2, which means . You will get the same answer that equals 2 by using the property that logb bx = x.
Logarithm of a Product
Remember that the properties of exponents and logarithms are very similar. With exponents, to multiply two numbers with the same base, you add the exponents. With logarithms, the logarithm of a product is the sum of the logarithms.
Logarithm of a Product
The logarithm of a product is the sum of the logarithms:
logb (MN) = logb M + logb N
Let’s try the following example.
Example
Problem
Use the product property to rewrite .
Use the product property to write as a sum.
Simplify each addend, if possible. In this case, you can simplify both addends.
Rewrite log2 4 as log2 22and log2 8 as log2 23, then use the property logb bx = x.
Or, rewrite log2 4 = y as 2y = 4 to find y = 2, and log2 8 = y as 2y = 8 to find y = 3.
Use whatever method makes sense to you.
Answer
Another way to simplify would be to multiply 4 and 8 as a first step.
You get the same answer as in the example!
log(a.b)=loga+logb(by formula)