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Linear Differential Equations of First Order

Solve the fol...

Question

Solve the following equation:
${log}_{3} (1 + {log}_{3} (2^{x} - 7)) = 1$

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Solution

${l o g}_{3} (1 + {l o g}_{3} (2^{x} - 7) = 1 \Rightarrow 1 + {l o g}_{3} (2^{x} - 7) = 3 \Rightarrow {l o g}_{3} (2^{x} - 7) = 2 \Rightarrow 2^{x} - 7 = 9 \Rightarrow 2^{x} = 16 \Rightarrow x = 4$

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