Question

Chapter - Laws of Indices

Solve for x :

$\bold{6^{2x+4}=3^{3x}.2^{x+8}}$​

Answer 1

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Answer 2

$heya \\ \\ \\ 6 {}^{2x + 4} = 3 {}^{3x} \times 2 {}^{x + 8} \\ \\ \\ \\ = > \\ \\ \\ (3 \times 2) {}^{2x + 4} = 3 {}^{3x} \times 2 {}^{x + 8} \\ \\ \\ = > \\ \\ \\ 3 {}^{2x + 4} \times 2 {}^{2x + 4} = 3 {}^{3x} \times 2 {}^{x + 8} \\ \\ \\ \\ = > \\ \\ \\ 3 {}^{ - x + 4} = 2 {}^{ - x + 4} \\ \\ \\ = > \\ \\ \\ \\ 3 {}^{ - x} \times 3 {}^{4} = 2 {}^{ - x} \times 2 {}^{4} \\ \\ \\ = > \\ \\ \\ (3 \div 2) {}^{ - x} = (3 \div 2) {}^{ - 4} \\ \\ \\ \\ x = 4$