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

Math, Linda has a total of 225 on 3 tests. The sum of the scores on the fir...

Linda has a total of 225 on 3 tests. The sum of the scores on the first and second tests exceeds her third score by 61. Her first test exceeds her second by 6 points. Find Linda''s

Ms. Pat, what is the simplified form of 5 square 32 - 4 square 18

what is the simplified form of 5 square 32 - 4 square 18

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?

Square Roots, What are the different ways to multiply/add/subtract/divide a...

What are the different ways to multiply/add/subtract/divide and work with square roots?

.., how do you round

how do you round

Example of exponential growth, Example The growth of a colony of bacteria ...

Example The growth of a colony of bacteria is provided by the equation,                                            Q = Q e 0.195 t If there are at first 500 bacteria exist

Eguations, I dont really understand it can you help me

I dont really understand it can you help me

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