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

Rational exponents, what is rational exponents and give some examples?

what is rational exponents and give some examples?

Decimals, in her last gymnastics competition Keri scored a 5.6 on the floor...

in her last gymnastics competition Keri scored a 5.6 on the floor exercise, 5.85 on the vault and 5.90 on the balance beam. what was keri''s total?

#variations., #If the common factor is known how do you find what the entir...

#If the common factor is known how do you find what the entire equation be (ex: A varies directly with t^2; A=8 when t=2. What is the formula?)

Factorisation, http://www.transtutors.com/live-online-tutor/math-help/

http://www.transtutors.com/live-online-tutor/math-help/

Find the zeros of a function, 3y+2.5x+3.4 use graphing calculator and the x...

3y+2.5x+3.4 use graphing calculator and the x intercept approach. Use window[-3,3,1][-3,3,1]

Determine dimensions of the field using quadratic equation, we are going to...

we are going to fence into a rectangular field & we know that for some cause we desire the field to have an enclosed area of 75 ft2. We also know that we desire the width of the fi

Mathematical definition absolute value equations, We can also indicate a st...

We can also indicate a strict mathematical/formula definition for absolute value.  It is, It tells us to look at the sign of p & if it's positive we just drop the absolute

Word problem change into alhebraic., I have 4.80 I need to separste into n...

I have 4.80 I need to separste into nichols, dimes and pennies. The first digit has to equal The first digist is l1 less the the first and the 2nd is once less than the third and

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