Already have an account? Get multiple benefits of using own account!
Login in your account..!
Remember me
Don't have an account? Create your account in less than a minutes,
Forgot password? how can I recover my password now!
Enter right registered email to receive password!
Properties of Logarithms
1. logb1 = 0 . It follows from the fact that bo = 1.
2. logb b = 1. It follows from the fact that b 1= b .
3. logb bx = x . it can be generalized out to blog b f ( x ) = f ( x ).
4. b logb x = x . It can be generalized out to b logb f ( x ) = f ( x ) .
Properties 3 and 4 lead to a pleasant relationship among the logarithm & exponential function.
Let's first calculate the following function compositions for f ( x )= b x and g ( x ) = logb x .
( f o g )( x ) = f [g ( x )] = f (logb x ) = b logb x = x
( g o f ) ( x ) = g [f ( x )]= g [b x ] = log b bx = x
Remember again from the section on inverse functions which this means that the exponential & logarithm functions are inverses of each other. It is a nice fact to remember on occasion.
We have to also give the generalized version of Properties 3 & 4 in terms of both the natural and common logarithm
ln e f ( x ) = f ( x) log10 f ( x ) = f ( x)
eln f ( x ) = f ( x ) 10log f ( x ) = f ( x )
Example Evaluate following logarithms. log 4 16 Solution Now, the reality is that directly evaluating logarithms can be a very complicated process, even for those who
-6k+7k=
head start
four hundred, sixteen million,forty-five
is (1,7),(2,7),(3,7),(5,7) a function
4x/y-3x/y+5x/y-x/y
Simpler method Let's begin by looking at the simpler method. This method will employ the following fact about exponential functions. If b x = b y then x
The population of a city was 141 thousand in 1992. The exponential growth rate was 1.6% per year. Find the exponential growth function in terms of t,where t is the number of years
Given f ( x ) = 3x - 2 find f -1 ( x ). Solution Now, already we know what the inverse to this function is as already we've done some work with it. Though, it would be n
what is the area of a polygon.
Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!
whatsapp: +91-977-207-8620
Phone: +91-977-207-8620
Email: [email protected]
All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd