FAD 1013

FAD 1013. INDICES, SURDS AND LOGARITHMS WEEK 1 (L2 & L3) Sir JEDZRY.

“exponent” or “index” (plural “indices”). “Base”.

5 appears 2 times.. It is possible for the exponent to be fractional, 0 or negative..

4. INDICES: Rules/Properties. abstract. abstract.

Simplify the following.. 1. Questions on provided worksheet..

Introduction to exponent. A black text with a white background Description automatically generated.

Rational roots. -3 is the 5th root of -243 since (-3)5 =-243..

8. EXAMPLE 1.

EXAMPLE 2.

[Audio] Remind students of the general form of each result where a is any number and m and n are integers..

11. SURDS. radical symbo radicand 2 index—O radical.

12. Properties of nth Roots Property = a if n is odd a I if n is even Example 16 2 3 (-5)3 = -5.

When simplifying expression related to surds, make sure to rationalise the denominator => get rid of the radical sign in the denominator..

EXAMPLE 3. Rationalize the following expressions..

EXAMPLE 4. Simplify the following:.

Log of x to the base a is y. abstract. Note: log of negatives and zero are not Defined in Reals.

Laws of Logarithms. PROPERTIES OF LOGARITHMS. abstract.

EXAMPLE 5.

EXAMPLE 6.

CHANGE OF BASE FORMULA-DERIVATION.

EXAMPLE 7.

SOLVING INDEX EQUATIONS.

EXAMPLE 8.

EXAMPLE 9.

EXAMPLE 10.

SOLVING RADICAL EQUATIONS. How to solve: Leave one of the terms with surd on one side and all other terms on the other. Square both sides of the equation and simplify. Repeat step 1 and step 2 if there is more than one term with surd (until all the surds are removed). Check the solution (true solutions of the original equation). Values which do not satisfy the equation = extraneous solutions (not a valid solution)..

EXTRANEOUS SOLUTION.

EXAMPLE 11.

SOLVING LOGARITHMIC EQUATIONS. The properties of log are used to simplify and solve the equations..

EXAMPLE 12.

EXAMPLE 13.

Reminder !!!!. Quadratic Equation is an equation with maximum degree of variable 2..

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