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

Shares and dividend, A man buys rs50 shares of a company paying 12% of divi...

A man buys rs50 shares of a company paying 12% of dividendat premium ofof rs10 find market value of 320 shares and profit%

Estimate how long did michael practice- algebra, Suppose that the number of...

Suppose that the number of hours Katie spent practicing soccer is represented through x. Michael practiced 4 hours more than 2 times the number of hours that Katie practiced. How l

Solid, The lateral edge of a pyramidal church spire is 61feet.Each side of ...

The lateral edge of a pyramidal church spire is 61feet.Each side of its octagonal base is 22feet. What will be the cost of painting the spire at 2.5 cents a square foot

Patrice has worked a certain how many hours has she worked, Patrice has wor...

Patrice has worked a certain amount of hours so far this week. Tomorrow she will work four more hours to finish out the week along with a total of 10 hours. How many hours has she

Number of permutations of ''n'' dissimilar things , Finding the numbe...

Finding the number of Permutations of 'n' dissimilar things taken 'r' at a time:  After looking at the definition of permutations, we look at how to evolve a

Applications of integrals, Applications of Integrals In this part we're...

Applications of Integrals In this part we're going to come across at some of the applications of integration.  It should be noted also that these kinds of applications are illu

Simplification, 4.4238/[1.047+{1.111*[9.261/7.777]}*1.01

4.4238/[1.047+{1.111*[9.261/7.777]}*1.01

Finding length and height with volume and width?, I figured out the volume ...

I figured out the volume and the width, but I have no idea how to use that information to get the height and the length!

Describe a business, a. Write an exponential function that could model the ...

a. Write an exponential function that could model the information in this graph.   b. Describe a business, scientific (not mathematical), or economic situation for what thi

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