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Question

Solve for x : ${2.9}^{x + 2} - {6.3}^{x + 1} = 0$ .

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Solution

${2.9}^{x + 2} - {6.3}^{x + 1} = 0 \Rightarrow {2.9}^{x + 2} = {6.3}^{x + 1} \Rightarrow {2.3}^{2 (x + 2)} = {6.3}^{x + 1} \Rightarrow {2.3}^{(2 x + 4) - (x + 1)} = 6 \Rightarrow 3^{(2 x + 4) - (x + 1)} = 3 \Rightarrow (2 x + 4) - (x + 1) = 1 \Rightarrow x = - 2$

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