There is an exclusive, Parent Information Page provides YOU with detailed reports of your child’s progress so you can monitor your child’s success and give them encouragement. These Reports include
Time spent using the program
Personalized remediation curriculum designed for your child
Details the areas of weakness where your child needs additional help
Provides the REASONS WHY your child missed a concept
List of modules accessed and amount of time spent in each module
Creates reports that can be printed and used to discuss issues with your child’s teachers
These reports are created and stored in a secure section of the program, available exclusively to you, the parent. The section is accessed by a password that YOU create and use. No unauthorized users can access this information.
Proof and Explanation of Formula 4 : Properties of Logarithms
Logarithm of any number to the same Base:
logaa = 1
Proof: From Laws of Exponents, we know a1 = a ⇒ logaa = 1 (Proved.)
It is easy to remember Logarithm of any number to the same Base is one.
Proof and Explanation of Formula 5 : Properties of Logarithms
Logarithm of a Product:
loga (mn) = logam + logan
Proof: Let logam = P ⇒ aP = m ............(i) Let logan = Q ⇒ aQ = n .............(ii) You might have observed that Equations (i) and (ii) are obtained by changing the Logarithmic form to Exponential form.
(i) x (ii) gives aP x aQ = mn ⇒ aP + Q = mn ( Since aP x aQ = aP + Q From laws of Exponents) ⇒ loga (mn) = P + Q ( by changing Exponential form to Logarithmic form) By Replacing the values of P and Q, we get loga (mn) = logam + logan (Proved.)
In proving this, see how we made use of changing Logarithmic to Exponential form and Exponential to Logarithmic form.
Remember that Logarithm of a Product is the sum of the Logarithms of the Factors of the Product.
Remember that the Formula is not for log(m + n) nor for log m x log n.
We have Formula for log (mn) and log m + log n.
We should be able to apply the formula from L.H.S. to R.H.S. and from R.H.S. to L.H.S.
Proofs and Explanations of Formula 6 to 10 : Properties of Logarithms
The following Link takes you to the Proofs and Explanations of Formula 6 to 10.
Progressive Learning of Math : Properties of Logarithms
Recently, I have found a series of math curricula (Both Hard Copy and Digital Copy) developed by a Lady Teacher who taught everyone from Pre-K students to doctoral students and who is a Ph.D. in Mathematics Education.
This series is very different and advantageous over many of the traditional books available. These give students tools that other books do not. Other books just give practice. These teach students “tricks” and new ways to think.
These build a student’s new knowledge of concepts from their existing knowledge. These provide many pages of practice that gradually increases in difficulty and provide constant review.
These also provide teachers and parents with lessons on how to work with the child on the concepts.
The series is low to reasonably priced and include