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

Solutions and linear combination, how do you find the solution using linear...

how do you find the solution using linear combinations 4x+3y=-1 and -3x+-5y=9

Word Problem, A student rented a bicycle for a one-time fee of $12.00 and t...

A student rented a bicycle for a one-time fee of $12.00 and then a charge of $0.85 per day.She paid $28.15 for the use of the bicycle. How many days did she keep it?

Pythagoras theorem, how do i find the length of the sides of a right triang...

how do i find the length of the sides of a right triangle

Non real complex components.., I need help solving the following Algebra pr...

I need help solving the following Algebra problem. Give all solutions of the nonlinear system of equations, including those with nonreal complex components. xy=-20 3x+5y=5

Solve, 15+1/2x=0.60(20+x)

15+1/2x=0.60(20+x)

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