The solving change of base formula is known as formulas which it permits us to rework a logarithm by means of the logs that may be is written with different base.
The change of base formula is given by,
Log a x = log b x / log b a
Here, assume that a, b and x are positive where a≠1 and b≠1.
Problem
Solve log 16 32
Change of base formula => loga x = logbx / logba
log 16 32 = log 2 32 / log 2 16
= 5 / 4
Thus a formula that allows you to rewrite a logarithm in terms of logs written with another base. This is especially helpful when using a calculator to evaluate a log to any base other than 10 or e.
In our next blog we shall learn "how to simplify radicals"
I hope the above explanation was useful.Keep reading and leave your comments.
In our previous blog we learned about Factor of 28. Today let us learn about "Factor of 72"
Like concepts presented throughout the Montessori classroom, even those more abstract concepts of Mathematics have been made concrete for the children in our classrooms. Beginning with simple number concepts like understanding quantity and identifying numerals, the Math materials include advanced presentations in cubing numbers, factors, fractions, and mathematical operations.
Factor Tree can be started by taking Different factors. The factor trees can be different but we will see that the Prime Factorization will remain same.
Steps to draw the Factor Tree of 72
Step 1: We start by building a Factor Tree of 72 by dividing 72 by smallest prime number that is 2.
Step 2: since 72 is 2 x 36 we write both these factors under 72 and circle 2 since it is prime.
Step 3: Since 36 is even number so we divide 36 again by 2 we get 2 x 18
Step 4: writing both factors 2 and 18 under 36 and circling 2 as it is again prime
Step 5: Then splitting 18 as 2 and 9 and writing the factors under 18 again circling the prime factor 2.
Step 6: Since now 9 is not divisible by 2 so we see next prime number that is 3
Step 7: On dividing it by 3 we get 3 which is the last and final factor.
Note: we keep on continuing these steps until we get all prime numbers in bottom row.
The Graphical representation of the factors of any number is called a Factor Tree
Factor Tree can be started by taking Different factors. The factor trees can be different but we will see that the Prime Factorization will remain same.
Steps to draw the Factor of 72
Step 1: We start by building a Factor Tree of 72 by dividing 72 by smallest prime number that is 2.
Step 2: since 72 is 2 x 36 we write both these factors under 72 and circle 2 since it is prime.
Step 3: Since 36 is even number so we divide 36 again by 2 we get 2 x 18
Step 4: writing both factors 2 and 18 under 36 and circling 2 as it is again prime
Step 5: Then splitting 18 as 2 and 9 and writing the factors under 18 again circling the prime factor 2.
Step 6: Since now 9 is not divisible by 2 so we see next prime number that is 3
Step 7: On dividing it by 3 we get 3 which is the last and final factor.
Note: we keep on continuing these steps until we get all prime numbers in bottom row.
In the above figure on the left side we see all the prime factors
So the prime factorization can be written as product of all Prime factors
72= 2 x 2 x 2 x 3 x 3
In simplified form it can be written in form of Exponents
72= 2^3 x 3^2
I hope the above explanation was useful.Keep reading and leave your comments.
Introduction to write quadratic function in vertex form
General form of a quadratic equation is y= ax2+ bx +c where a,b and c are real numbers and a 0.The graph of the quadratic equation is a parabola (either up or down). Let us assume that this parabola has its vertex at (h,k), then we can write the quadratic equation in vertex form as y= a(x-h)2+k.
There are 2 methods to write quadratic equation in vertex form.
Click on the link to learn about "quadratic equation formula"
1. Using completing the square method
2. Using vertex formula
VERTEX : For any two edges that meet at an end – point, there is a third edge, that also meets them at that end – point. This point of intersection of three edges of a cuboid is called a vertex of the cuboid.
The vertices of the cuboid in the figure are A, B, C, D, E, F, G, H.
Clearly, a cuboid has 8 vertices.
Thus, we see that the twelve edges of a cuboid can be grouped into three groups such that all edges in one group are equal in length. This means that twelve edges of a cuboid can have only three distinct lengths. Usually, the longest of these is called the length of the cuboid and out of the remaining two, one is called the breadth or width and the other height of the cuboid.
BASE AND LATERAL FACES : Any face of a cuboid may be called the base of the cuboid. In that case, the four faces which meet the base are called the lateral faces of the cuboid.
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Let us learn about "Antiderivative Calculator" and as you know in previous blog we learned about "Molarity Calculator" which was very interesting.
Antiderivative Calculator allows users to enter an integrand in order to return the indefinite integral. Does anybody know something about antiderivative solver online? Integral Calculator calculates an antiderivative (indefinite integral) of a function with respect to a given variable using analytical integration. The first thing is the antiderivative you will usually learn, when you begin your study of integral calculus.
As simple we can say, antiderivative finding is the exact opposite process of finding the derivative of any given function. So, before beginning a study of integral calculus, you must have a firm foundation in differential calculus. For an algebraic equation solver, antiderivative finding process is not very complex.
I hope the above explanation was useful. Keep reading and leave your comments.
* Common Factor
* Prime Factor
* Highest Common Factor
Let Us understand About Common Factor
10 = 2 × 5 = 1 × 10
Thus, the factors of 10 are 1, 2, 5 and 10.
15 = 1 × 15 = 3 × 5
Thus, the factors of 15 are 1, 3, 5 and 15.
Clearly, 5 is a factor of both 10 and 15. It is said that 5 is a common factor of 10 and 15. We shall Learn About Prime Factor in our next blog
Subtraction is the operation which finds the difference between the given two numbers. This is also one of the basic operations. There are two terms used in subtraction they are minuend and subtrahend. Where minuend is the term to be subtracted and subtrahend is the term which subtracts the minuend. When the value of the minuend is greatest then the result is positive. When the value of the subtrahend is greatest then the value is negative.
Subtraction Formula:
We shall learn on subtraction formula. The fixed names for the parts of the formula:
c − b = a
Are minuend(c) –subtrahend (b) = difference (a).
As a substitute that c and −b are terms, and subtract as addition of the opposite. The solution is still called the difference.
As a substitute that c and −b are terms, and subtract as addition of the opposite. The solution is still called the difference.
Let us understand with examples
The following problems are simple subtraction.
1) 9 - 9 = 0
The value 6 minus value 6 equal to 0
The solution is 0(zero).
2) 12 – 24 = - 12
The value 12 minus value 24 equal to minus 12
The solution is minus 12
3) 6 – 4 = 2
The value 6 minus value 4 equal to 2
The solution is 2
4) 10 – 7 = 3
The value 10 minus value 7 equal to 3
The solution is 3
5) 5.3 – 1.1 = 4.2
The decimal value 5.3 minus decimal value 1.1 equal to 4.2
Let us learn about "change of base formula"
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0.The graph of the quadratic equation is a parabola (either up or down). Let us assume that this parabola has its vertex at (h,k), then we can write the quadratic equation in vertex form as y= a(x-h)2+k.
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