Properties of exponential form, Mathematics

Assignment Help:

Properties

1.   The domain of the logarithm function is (0, ∞ ) .  In other terms, we can just plug positive numbers into a logarithm! We can't plug in zero or a negative number.

2.    logb b = 1

3.    logb 1 = 0

4.    logb bx= x

5.    blogb= x

The final two properties will be especially useful into the next section.  Notice that these last two properties tell us that,

f( x ) = b x              and g( x ) = logb x

are inverses of each of other.

Following are some more properties which are useful in the manipulation of logarithms.

More Properties

6.   logbxy= logb  x + logb  y

7.   logb (x/y)=       logb  x - logb  y

8.   logb( xr) = r logb  x

Note as well that there is no equivalent property to the first two for sums & differences. In other terms,

logb( x + y ) ≠ logb  x + logb  y

logb(x - y ) ≠ logb  x - logb  y


Related Discussions:- Properties of exponential form

Determine the max theoretical information rate, 1 Data is to be transmitted...

1 Data is to be transmitted over Public Switched Telephone Network (PSTN) using 8 levels per signaling elements. If the bandwidth is 3000 Hz, deduce the theoretical maximum transfe

Related to MCA, AskIf y=e^(a?sin?^(-1) x), prove that (1 – x2)yn+2 – (2n + ...

AskIf y=e^(a?sin?^(-1) x), prove that (1 – x2)yn+2 – (2n + 1)xyn+1 – (n2 + a2)yn = 0. Hence find the value of yn when x = 0. question #Minimum 100 words accepted#

#titlefunction.., provide a real-world example or scenario that can be expr...

provide a real-world example or scenario that can be express as a relation that is not a function

Operation on polynomial, Perform the denoted operation for each of the foll...

Perform the denoted operation for each of the following.  (a) Add 6x 5 -10x 2 + x - 45 to 13x 2 - 9 x + 4 .   (b) Subtract 5x 3 - 9 x 2 + x - 3 from       x 2+ x +1.

Relate Fractions and Whole Numbers, Jon ran around a track that was one eig...

Jon ran around a track that was one eighth of a mile long.He ran around the track twenty four times.How many miles did Jon run in all

Laws of indicies in fraction.., help to solve the laws of indicies chapter ...

help to solve the laws of indicies chapter 9c book 3 high school example19to the power3_2 what is answer

Rates of change or instantaneous rate of change, Rates of Change or instant...

Rates of Change or instantaneous rate of change ; Now we need to look at is the rate of change problem.  It will turn out to be one of the most significant concepts . We will c

representative value or an extreme value, A population forms a normal dist...

A population forms a normal distribution with a mean of μ=80 and a standard deviation of o=15. For every samples, compute the z-score for the sample mean and determine whether the

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