Solve for x : (a 3x + 5 ) 2 .(a x ) 4 = a 8x + 12

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Mathematics

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Given,

⇒ (a^{3x + 5})².(a^x)⁴ = a^{8x + 12}

⇒ a^{2(3x + 5)}.a^4x = a^{8x + 12}

⇒ a^{6x + 10}.a^4x = a^{8x + 12}

⇒ a^{6x + 10 + 4x} = a^{8x + 12}

⇒ a^{10x + 10} = a^{8x + 12}

⇒ 10x + 10 = 8x + 12

⇒ 10x - 8x = 12 - 10

⇒ 2x = 2

⇒ x = $\dfrac{2}{2}$ = 1.

Hence, x = 1.

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