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

Standard deviation, what is the standard deviation of a graph

what is the standard deviation of a graph

Write & Solve Equations, Lisa and Judy read mystery novels. Judy has read ...

Lisa and Judy read mystery novels. Judy has read three fewer than five times as many as Lisa. Equation: J=5L-3 Lisa: Judy:

Prime factorization tree method, I am trying to figure out how the tree met...

I am trying to figure out how the tree method works for number 47

Problem solving .use multiplacation, ellie uses 12.5 pounds of potatoes to ...

ellie uses 12.5 pounds of potatoes to make mashed potatoes. she uses one-tenth as many pounds of butter as potatoes. how many pounds of butter does ellie use

Verticies, how many does a rhombus have

how many does a rhombus have

Kelsey, my homework instructions are "solve by factoring" and one of the pr...

my homework instructions are "solve by factoring" and one of the problems is 2x^2+9x=0

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