Equations Involving Indices (Leaving Cert Mathematics): Flashcards

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Equations Involving Indices
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Equations involving indices

Equations where the variable is an exponent

If ax=aya^x = a^y, then...

x=yx = y

First step to solve index equations

Express both sides as powers of same base

Formula for a−na^{-n}

1an\frac{1}{a^n}

(am)n(a^m)^n equals

amna^{mn}

a\sqrt{a} as fractional index

a12a^{\frac{1}{2}}

What negative indices represent

Reciprocals

Express 25 as a power of 5

525^2

Express 125 as a power of 5

535^3

Simplify 8\sqrt{8}

222\sqrt{2}

Simplify 27\sqrt{27}

333\sqrt{3}

How to verify solution to index equation

Substitute answer back into original equation

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