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4.3 Equations Involving Indices

January 21, 2022April 25, 2020 by

METHOD:

Comparison of indices or base

If the base are the same , when $a^{x} = a^{y}$ , then x = y
If the index are the same , when $a^{x} = b^{x}$ , then a = b

Using common logarithm (If base and index are NOT the same)

$\begin{array}{l} a^{x} = b \Rightarrow \lg a^{x} = \lg b \\ x = \frac{\lg b}{\lg a} \end{array}$

Example 1 (Index Equation – Equal base)
Solve each of the following.
(a)

$16^{x} = 8$
(b)

$9^{x} {.3}^{x - 1} = 81$
(c)

$5^{n + 1} = \frac{1}{125^{n - 1}}$

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