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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.
6th-8th Foundation

### Exponents

Welcome to the astonishingly clear introduction to exponents, roots, and logarithm. Learn in this

•  representation of exponents

•  roots and logarithms are two inverses of exponents

•  difference between common and natural logarithms

•  arithmetics with exponents and logarithms

•  Precedence -- PEMDAS or BODMAS (Exponent and Order)

•  introduction to squares and square roots

•  introduction to cubes and cube roots

All the above are given in a simple thought process.
(click for the list of lessons in this topic)

Fundamentals of Exponents

Welcome to the astonishingly clear introduction to exponents, roots, and logarithm. Learn in this

•  representation of exponents

•  roots as one inverse of exponents -- finding base from given power and exponent result

•  logarithms as the another inverse of exponents -- finding power from the given base and exponent result

This clarity is essential to understand the properties of roots and logarithms.

In this, common and natural logarithms are introduced. To explain natural logarithm, the number e is introduced in a thought-provoking and revolutionary discourse.

(click for the list of pages in the lesson)

Exponents and Logarithm Arithmetics

Exponents are repeated multiplication. Root is an inverse of exponent to find the base. Roots are also considered as a form of exponent with fraction power. Logarithm is another inverse of exponent to find the power. This page explains arithmetics with exponents and logarithms -- providing a list of formulas as known results or properties.

At the end, the roots and logarithms that are not defined are explained. For example: log_0 a and log_1 a are not defined. root(0)(a) is not defined.

(click for the list of pages in the lesson)

The pages in this lesson are

Numerical Expressions with Exponents

Do you want to understand how the exponents, roots, and logarithms are handled in numerical expressions?

In this lesson, learn the following.

•  precedence order : PEMDAS or BODMAS

•  sequence of operations : left to right

Most importantly, learn handling of root and logarithm as inverse of exponent.

(click for the list of pages in the lesson)

The pages in this lesson are

Squares and Square Roots

Squares and Square roots are explained in a simple-thought-process. This also covers finding square root using prime-factorization and long division methods.

(click for the list of pages in the lesson)

Cubes and Cube Roots

Cubes and cube roots are explained in a simple-thought-process. This also covers finding cube roots using prime-factorization.

(click for the list of pages in the lesson)

The pages in this lesson are