There we discussed the need for extension of Exponents and introduction to the new branch of study.

It is a prerequisite here.

Here, we will study Various Formulae and provide links to further study.

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In the following formulas, the base of the log is positive real number (≠ 1). When we write log of a literal, that literal is a positive real number.

Log Formula 1 : Formula from definition of Log:

a^{x} = n ⇔ log_{a}n = x

Log Formula 2 : Log as an Exponent to its Base:

a^{loga n} = n

Log Formula 3 : Log of 1 to any Base:

log_{a} 1 = 0

Log Formula 4 : Log of any number to the same Base:

log_{a}a = 1

Log Formula 5 : Log of a Product:

log_{a} (mn) = log_{a}m + log_{a}n

Log Formula 6 : Log of a Quotient:

log_{a} (m⁄n) = log_{a}m - log_{a}n

Log Formula 7 : Log of a Power:

log_{a} (m^{n}) = n log_{a}m

Log Formula 8 : Change of Base of a Log :

log_{a}b = (log_{k}b)⁄(log_{k}a)

Log Formula 9 : Log of a Power to the Base of another Power:

log_{an} (b^{m}) = (m⁄n) log_{a}b

Log Formula 10 : Log of b to the base a; b and a interchanged:

log_{a}b = 1⁄(log_{b}a)

All the above 10 Formulas are to be remembered and to be appliedto solve various problems. What we said about Formulas andproblems in
Exponents
holds good here also. We repeat that here.

The best way to remember various Algebra Formulas(or Math Formulas) is to apply them to a number of problems.The best way to solve Algebra Problems (or Math Problems) is to remember various formulas.

Put an effort to remember the Formulas. Don't worryeven if you are not 100% perfect. Go ahead with the problemsin the set of worked out examples and the Exercise ofLogarithms given below (after the Proofs and explanationsof the 10 Formulas). Applying the Formulas to variousproblems will help you in remembering the Formulas.You can study the proofs given below, now or after masteringthe Formulas and their application to various problems.The choice is yours.

Proofs and Explanations of the Formulas :

The Proofs and Explanations for the above Formulas in Logarithms are provided at the following Links.

To find the log value of a number using Tables we need the knowledge of Charateristic and Mantissa which is covered in
Logarithm Tables.

Exercise : Logarithms

The above Five Sets of Examples also contain Exercise problems.

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