Last updated on Oct 23, 2026

Solving Equations with Indices (Leaving Cert Mathematics): Quizzes

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Solving Equations with Indices

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When bases are equal in $a^x = a^y$ , what can you do?

Cancel bases and solve $x = y$

Solve $3^{x+5} = 3^{2x}$

$x = 5$

Why does canceling equal bases work in $a^x = a^y$ ?

Take logarithm of both sides

To solve $2^{x^2} = 8^{2x+9}$ , what should you do first?

Rewrite $8$ as $2^3$

What is $8$ written as a power of $2$ ?

$2^3$

What does $(a^p)^q$ equal?

$a^{pq}$

When is substitution used for exponential equations?

When rewriting the base isn't simple

In $2^{2y+1} - 5(2^y) + 2 = 0$ , what substitution is made?

Let $2^y = a$

After solving for the substituted variable, what must you do?

Resubstitute the original expression

If $2^y = \frac{1}{2}$ after substitution, what is $y$ ?

$y = -1$

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