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

Complex fractions, how do I do complex fractions X over 25 over x over 15

how do I do complex fractions X over 25 over x over 15

Uniform motion, How do you do uniform motion? i am stuck on some problems

How do you do uniform motion? i am stuck on some problems

Simplifying and solving radicals, I have an algebra test tomorrow and still...

I have an algebra test tomorrow and still don''t understand how to simplify and solve radicals

Graphing, the problem is 6x+3y=-24. is tells me to graph using y=mx+b forma...

the problem is 6x+3y=-24. is tells me to graph using y=mx+b format but i don''t know how to get to that point.

Britt, #ques1). Using the function: y=y0,(.90)^t-1. In this equation y0 is ...

#ques1). Using the function: y=y0,(.90)^t-1. In this equation y0 is the amount of initial dose and y is the amount of medication still available t hours after drug is administered.

Household Water Use, During a recent rainy day, 72 mm of rain was recorded....

During a recent rainy day, 72 mm of rain was recorded. Calculate how many litres of water will be collected from the roof and stored in the water tank. Remember The volume V

Factoring.., w^2 + 30w + 81= (-9x^3 + 3x^2 - 15x)/(-3x) (14y = 8y^2 + y^3 +...

w^2 + 30w + 81= (-9x^3 + 3x^2 - 15x)/(-3x) (14y = 8y^2 + y^3 + 12)/(6 + y) ac + xc + aw^2 + xw^2 10a^2- 27ab + 5b^2 For the last problem I have to incorporate the following words

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