Properties of logarithms, Algebra

Assignment Help:

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 )


Related Discussions:- Properties of logarithms

Convert following into the function, Convert following into the form    ...

Convert following into the form                                        f (x ) = a ( x - h ) 2  + k Solution We are going to complete the square here.  Though, it is a s

Quiz #5., Working together Jack and Bob can clean a place in 30 minutes. On...

Working together Jack and Bob can clean a place in 30 minutes. On his own, Jack can clean this place in 50 minutes. How long does it take Bob to clean the same place on his own?

Solve the given log function, Example: Solve following equations. 2 log...

Example: Solve following equations. 2 log 9 (√x) - log 9 (6x -1) = 0 Solution  Along with this equation there are two logarithms only in the equation thus it's easy t

Solving for a variable, what are the steps to solving a variable like this ...

what are the steps to solving a variable like this one -3f=g for f

Percents, How do I figure out what is 20% of 100?

How do I figure out what is 20% of 100?

Pre algebra, i need help with linear functions in pre algebra i have a tes...

i need help with linear functions in pre algebra i have a test tomorrow and i need help with the concept and ways to remeber it thank you! mackenzie

Expressions and inequlites, A blue whale gains 2.3 tons a month for the fir...

A blue whale gains 2.3 tons a month for the first year of life. If a blue whale weighed 15 tons at birth, how much will it weigh on its first birthday?

Logarithms, Log(8)10 Find the approximation and exact value. log(5)317 Fi...

Log(8)10 Find the approximation and exact value. log(5)317 Find the approximation and exact value

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

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!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd