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

Rings homomorphisms, if A is an ideal and phi is onto S,then phi(A)is an id...

if A is an ideal and phi is onto S,then phi(A)is an ideal.

Geometry, how do you do proofs?

how do you do proofs?

Methods for solving systems equations, Methods for solving systems We w...

Methods for solving systems We will be looking at two methods for solving systems in this section. Method of substitution The first method is known as the method of sub

Formula, using the formula for the difference between two squares,factor th...

using the formula for the difference between two squares,factor the following : 5-x

I need help with my cahsee, Ask questionteachme how to graph points convert...

Ask questionteachme how to graph points convert fractions to deciams #Minimum 100 words accepted#

Math class help, Hi I need help for the next 4weeks with my online math cla...

Hi I need help for the next 4weeks with my online math class I have included one assignment instruction below if you can help me please give me a quote I also have math labs that I

AS/A2 Coursework, I need to do a coursework for math but do not know what t...

I need to do a coursework for math but do not know what to do?

Polynomial inequalities, Now it is time to look at solving some more hard i...

Now it is time to look at solving some more hard inequalities.  In this section we will be solving (single) inequalities which involve polynomials of degree at least two.  Or, to p

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