Indices (Leaving Cert Mathematics): Flashcards

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Solving Equations with Indices
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Equal bases in exponential equations

Cancel bases, equate the powers

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

x=yx = y

Why can equal bases be cancelled?

Take logarithm of both sides to eliminate base

Technique when bases differ

Rewrite to have same base

Index law: (ap)q=?(a^p)^q = ?

apqa^{pq}

Index law: ap+q=?a^{p+q} = ?

apcdotaqa^p cdot a^q

Substitution technique for complex indices

Let power term = variable, solve, then resubstitute

After solving with substitution

Resubstitute the original expression

Express 88 as power of 22

232^3

Solve 2x+8=25x2^{x+8} = 2^{5x}: first step

Cancel bases: x+8=5xx+8 = 5x

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