Lesson 8, Topic 1
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# Exponential Equations

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The various laws of indices are also of importance in solving simple exponentials given below:

Example

Solve the following equations:

(a) $$\scriptsize 5^{2x – 4} = 25 ^{-x – 8}$$

(b) $$\scriptsize 8^x = 0.125$$

(c) $$\scriptsize p^x = \normalsize \frac{ \sqrt[4] {p^5}\: \times \: p^{- \frac{1}{4}}}{ \left(\sqrt [3] {p}\right)^2}$$

(d) $$\frac {1}{4} \scriptsize \; of \; 64x = 16^{3x}$$

(e) $$\scriptsize 9^{x – 3} = 27 ^{x – 5}$$

(f) $$\scriptsize 9^{2x + 1} = \normalsize \frac {81 ^{x – 3}}{3^x}$$

(g) $$\scriptsize 7(8^{x + 1}) = 448$$

(h) $$\left(\frac {5}{6}\right)^{ \frac{1}{2}} = \left(\frac {6}{5}\right)^{x – 1}$$

(i) $$\frac {64}{27} = \left(\frac {3}{4}\right )^{^{\normalsize x – 1}}$$

Evaluation:

Solve the following;

(i) $$\scriptsize 9^{2x} = \normalsize \frac{81^{x-2}}{3^x}$$

(ii)$$\scriptsize 2^{2x} \: – \: 3\: \times \: 2^x \: + \: 2 = 0$$

error: