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

Two forms of the parabola, There are two forms of the parabola which we wil...

There are two forms of the parabola which we will be looking at. The first form will make graphing parabolas very simple.  Unluckily, most parabolas are not in this form.  The seco

Example of synthetic division, Using synthetic division do following  divis...

Using synthetic division do following  divisions. Divide 2x 3 - 3x - 5  by x + 2 Solution Okay in this case we have to be a little careful here. We have to divide by a

Percentages, in a cloths shop reduces it prices by 20% how much is it on sa...

in a cloths shop reduces it prices by 20% how much is it on sale

Multiply a row by a constant, Multiply a Row by a Constant.   In this opera...

Multiply a Row by a Constant.   In this operation we multiply row i by a constant c and the notation will utilizes here is cR i .  Note that we can also divide a row by a constant

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